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HIGH RESOLUTION RUTHERFORD BACKSCATTERING SPECTROSCOPY:

HAFNIUM BASED HIGH-K DIELECTRIC THIN FILMS AND SIMULATION OF 2-D

FOCAL PLANE DETECTOR

TAY XIU WEN

A THESIS PRESENTED FOR THE DEGREE OF BACHELOR OF SCIENCE

DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE

2014

Table of Contents

ii

Table of Contents Acknowledgements .............................................................................................................................iv

Summary .............................................................................................................................................v

List of Figures.......................................................................................................................................vi

Chapter 1 : Introduction....................................................................................................................... 1

1.1 High Resolution Rutherford Backscattering Spectrometry.....................................................................1

1.2 New generation of two dimensional position detector .........................................................................1

1.3 Swift Heavy Ion irradiaton of HfO2/Si ultra thin film………………………….......................………………………...2

1.4 Outline of thesis ………………................................................................................................................…..3

Chapter 2 : Physical Concepts ...............................................................................................................4

2.1 Kinematic Factor………………………………………………………….........................................................................4

2.2 Rutherford Scattering Cross Section………………..............................................................………………………7

2.3 Deviation from Rutherford Scattering ……………..................................................……………………….………10

2.4 Stopping cross section………….........................................................................................................…….11

2.5 Energy Straggling……………......................................................................................................…………….13

2.6 Rutherford Backscattering Spectrometry.............................................................................................15

2.7 Ion Channeling…………………….................................................................................................….…………16

2.8 Thin film on substrate…........................................................................................................................17

2.9 SIMNRA Numerical Simulation of RBS spectrum…………………......………....................………….……..………19

Chapter 3 : HRBS Set-up ....................................................................................................................21

3.1 HRBS Endstation………………………………………...................................................................……….…………...21

3.1.1 Main chamber, load lock and vacuum system……………………………………..............................…………….22

3.1.2 Goniometer…………………………………….............................................................................................…..24

3.1.3 Micro-channel Plates……….………………................................................................................................25

3.2 Electrostatic plates...............................................................................................................................26

3.3 1-D Focal Plane Detector and HRBS electronics……………………….............................................…………..26

3.3.1 2-D Focal Plane Detector..................................................................................................................28

Table of Contents

iii

Chapter 4 : Study of Swift Heavy Ion Irradiation effects on Hafnium based high k-dielectric thin films

deposited on Silicon...........................................................................................................................29

4.1 Swift Heavy Ion ……………………………………………….................................................................……………….29

4.2 Ion beam Mixing…………………………………….................................................................................………...29

4.3 HfO2/SiO2/Si Samples …………………...........................................................................................…………30

4.4 HRBS experimental parameters...........................................................................................................31

4.5 HRBS Depth profiling results................................................................................................................31

4.6 Conclusion………………………………………..........................................................................................……...36

Chapter 5 : Simulation and characterisation of new 2-D focal plane detector using SIMion ................82

5.1 2-D Focal Plane Detector………............................................................................................................37

5.2 Overall layout of the HRBS detection system……………………....................................................………….39

5.3 Spectrometer ion optics……….........................................................................................................…..40

5.3.1 Beam entry parameters…….............................................................................................................40

5.3.2 Drawing the magnet……………………...................................................................................................42

5.3.3 Maxwell’s and Laplace’s equations………….…...............................................................................…..43

5.3.4 Refining the magnet array …………………………....................................................................................44

5.3.5 Finite Difference Method ……………….................................................................................................44

5.3.6 Calculation of ion trajectories ………........................................................................................………..45

5.4 SIMion simulation details ………………….................................................................................……...........47

5.5 SIMion simulation results………………….................................................................................……………..48

5.5.1 Splat profiles……….......................................................................................................………….………..48

5.5.2 Height and Width of splat profiles………............................................................................................51

5.5.3 Variations in starting x-position of backscattered ions……….........................................................….53

5.6 Simulation Conclusion……….......................................................................................................……….55

Bibliography ....................................................................................................................................57

Appendices ......................................................................................................................................59

Acknowledgements

iv

Acknowledgement

I would first like to thank my supervisor Associate Professor Thomas Osipowicz who has been a

great mentor and with his careful guidance, has made this thesis possible. I am also thankful of

his patience and the time he spent to guide my work despite his busy schedule. I am also very

grateful to Dr TK Chan who taught me almost everything I know about RBS and HRBS as well as

various laboratory techniques.

I would also like to thank my life mentors, Sumithra and Lionel for their love and trust for which

without them, this thesis would not be possible. Last but not least, I would like to thank my

family for their unwavering support and my deceased father whose memory will always live on

in my heart.

Abstract

v

Abstract

Due to advancement in the miniaturization of microelectronic components, conventional Rutherford

Backscattering Spectrometry (RBS) can no longer provide sufficient depth resolution for ultra-thin films.

The High-resolution RBS (HRBS) system in CIBA allows thin film depth profiling of such films with a

modified RBS system where the differentiation of energy of the backscattered ions is achieved by

spectrometer magnet and a Micro- Channel Plate-Focal Plane Detector (MCP-FPD) detection system.

The backscattered ions travel through the spectrometer magnet with different ion trajectories according

to their energy are subsequently incident on the MCP-FPD at the focal plane. The energy of the

backscattered ion is then determined by the MCP-FPD and subsequent HRBS electronics

In modern microelectronics, thickness of SiO2 gates dielectrics reach the subnanometer range with the

increasing miniaturization of Metal-Oxide Field Emission Transistors (MOSFETs). Thicker dielectric

materials with higher dielectric constants (high-k dielectrics) must be used to reduce the leakage

current, retaining the same capactitative density of a thinner layer of SiO2. In recent years, other high-k

material such as HfO2 have been used and studied for their properties as gate dielectrics. In the first part

of the thesis, ultra-thin HfO2/SiO2/Si samples of increasing irradiated fluence of Au Swift Heavy Ions films

were characterized using HRBS depth profiling. HRBS measurements suggest that the interlayer is a

mixed HfSiO/SiO layer instead of a pure SiO2 layer as intended. A systematic increase in thickness of the

interlayer as a function of increasing fluence of Au swift heavy ions.

In current HRBS analysis, a 1-D focal plane detector is used to profile the detected backscattered ions

according to backscattered ion energy. However, in preparation of future hardware upgrade, a 2-D FPD

is proposed to profile splat profiles of the end of the ion trajectories in both directions of the FPD; along

the height as well as length of the FPD. Hence, in the last part of the thesis, SIMion simulations were

done to characterize the 2-D splat profiles on the FPD. The simulations shows that height of splat

profiles for 2mm collimeter is below 8mm and for 1mm collimeter, it is below 4mm. Hence, the splat

profiles are able to fit into the 15mm height of the 2-D FPD. It is also observed that at least 50 splat

profiles of 50 different ion energies (2mm collimeter) or at least 100 splat profiles of 100 different ion

energies (1mm collimeter) can be fitted into the 100mm length of the FPD.

List of Figures

vi

List of Figures

Fig. 2.1 Elastic collision diagrams as seen in the (a) lab reference frame (b) CM reference frame. [7].......5

Fig. 2.2 Fig. 2.2 Plot of F ( , Ec) vs . Correction magnitude increases rapidly at small and decreases

with increasing E0 at large . Source [8]....................................................................................................11

Fig. 2.3 Plot of Chu correction factors H vs Z2 for various E/M1 values. Dots are original data from Chu

and the lines are extrapolations by Szilágyi [9]. Source [7]........................................................................14

Fig. 2.4 Diagram of RBS measurement.......................................................................................................15

Fig. 2.5 Schematic of ion channeling. Source [10].....................................................................................15

Fig. 2.6 (a) Schematic of the formation of the shadow cone at the surface and the trajectories of

channeled particles. The horizontal scale on the right is compressed in relation to the vertical scale to

show the trajectory oscillations. (b) The comparison between the channeled and the non-aligned RBS

spectrum. The channeled spectrum shows a drastically reduced substrate signal. Source [10] ..............17

Fig. 2.7 (a) Scattering geometry and (b) spectrum of an RBS measurement of a thin compound target

Source [11] ................................................................................................................................................17

Fig. 2.8 Diagram of the target divided into thin layers. Source [11]..........................................................19

Fig. 3.1 (a) Main chamber, goniometer and load lock. (b) Load lock with a sample holder (c) View of

sample holder on the goniometer in the main chamber through the main viewport. Source [11] .........22

Fig. 3.2 Schematic of the vacuum pump and valve network. Source [11] ...............................................23

Fig. 3.3 Schematic of the HRBS goniometer. Source [12] ........................................................................24

Fig. 3.4 Diagram of Micro-channel plates ................................................................................................25

Fig. 3.5 Schematic and layout of the installation of the electrostatic plates. Source [11] ......................26

Fig. 3.6 Schematic of 1-D Focal Plane Detector and HRBS electronics. Source [11] ................................27

Fig. 4.1 Sample structure of Pristine-H1A................................................................................................31

List of Figures

vii

Fig. 4.2 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation of Pristine-

H1A sample...............................................................................................................................................32

Fig. 4.3 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1B-1E13 Au

sample.......................................................................................................................................................32

Fig. 4.4 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-5E13 Au

sample.......................................................................................................................................................33

Fig. 4.5 Aligned(Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-1E14 Au

sample.......................................................................................................................................................33

Fig. 4.6 Aligned(Channeled) HRBS spectra of Hafnium peak for all four samples (H1A, H1B, H1C, H1D)..34

Fig. 4.7 Elemental depth profile for H1A, H1B, H1C, H1D.........................................................................35

Fig 5.1 Diagram of 2-D FPD with true counts (red dotted ovals) and counts derived from HRBS (black

ovals).........................................................................................................................................................37

Fig. 5.2 Schematic of simulation done using SIMion.................................................................................38

Fig. 5.3 Schematic of Spectrometer magnet, MCP-FPD in HRBS. Source [11]...........................................39

Fig. 5.4 Schematic of the incident and backscattered beam profiles........................................................41

Fig. 5.5 Finite backscattered beam profile and point source approximation............................................41

Fig. 5.6 3-D isometric view of the workbench with a magnified view of the spectrometer magnet. Source

[11]............................................................................................................................................................43

Fig 5.7 Diagram depicting “Finite Difference Method (FDM)"..................................................................45

Fig. 5.8 The potential distribution plot along the x-y plane at a fixed value of z. The darkened flat top

represents the region with uniform magnetic field , while the smooth slopes at the sides represent the

non-uniform fringe fields. Source [11] .....................................................................................................45

Fig. 5.9 The overview of the workbench in the x-y plane looking down towards the negative z-direction.

Source [11]................................................................................................................................................47

Fig. 5.10 Splat profile for a point spot and beam spot of E = 427keV collimated by a 1mm collimeter...48

List of Figures

viii

Fig. 5.11 Splat profiles of a point spot of energy, E from 400 keV to 421 keV simulated through 1mm

collimeter.................................................................................................................................................. 49

Fig. 5.12 Splat profiles of a point spot of energy, E from 421 keV to 442 keV collimated by 1mm

collimeter ..................................................................................................................................................50

Fig. 5.13 Height of the splat profiles for point and beam spots collimated by 2mm collimeter ...............51

Fig. 5.14 Width of the splat profiles for point and beam spots collimated by 2mm collimete..................52

Fig. 5.15 Height of the splat profile of the double focusing point at different starting x-position of the

backscattered ion (2mm collimeter) ..........................................................................................................53

Fig. 5.16 Width of the splat profile of the double focusing point at different starting x-position of the

backscattered ion (2mm collimeter) ..........................................................................................................54

Fig. 5.17 Centre position of the splat profile of the double focusing point at different starting x-position

of the backscattered ion (2mm collimeter) ...............................................................................................54

Fig. A.1 Figure Splat profiles of a point spot of energy, E from 400 keV to 421 keV simulated through

2mm collimeter .........................................................................................................................................59

Fig. A.2 Splat profiles of a point spot of energy, E from 421 keV to 442 keV collimated by 1mm collimeter

...................................................................................................................................................................60

Fig. A.3 Height of the splat profiles for point and beam spots collimated by 2mm collimeter ...............60

Fig. A.4 Width of the splat profiles for point and beam spots collimated by 2mm collimeter ................61

Fig. A.5 Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)..........................................................................................................62

Fig. A.6 Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)..........................................................................................................62

Fig. A.7 Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter )...............................................................................................63

Introduction Chapter 1

1

Chapter 1

Introduction

1.1 High Resolution Rutherford Backscattering Spectrometry

Rutherford Backscattering Spectroscopy is a non-destructive method which is mainly used for

depth profiling of thin films. The PIPS detector used in conventional RBS to detect

backscattered ions is only able to provide a depth resolution of up to 5nm at glancing

geometry. However with ultra-thin films with order of tens of angstrom, conventional

Rutherford backscattering is not able to provide adequate depth profiling.

In order to quantify the depth profile of ultra thin films, a high resolution Rutherford

backscattering spectrometry (HRBS) system is used [21]. In HRBS, the PIPS detector is replaced

by a spectrometer-focal plane detector. This provides a better resolution (circa 1KeV) and

subnanometer depth resolution. HRBS is useful for depth profiling of thin films eg. Gate

dielectric films in semiconductor devices. Combined with channeling technique, it can also

provide information on dopant position in crystal lattices, lattice strain and stress.

1.2 New generation of two dimensional position detector

In the current HRBS facility, a one dimensional focal plane detector is used to detect the

backscattered ions and measure their backscattered ion energy. 1-D FPD measures only the

position of the incident ions in the dispersion plane of the magnet, all the ions incident

perpendicular to this direction are summed over and this may lead to spectral distortion


2

effects. In preparation of a future hardware upgrade, a 2-D FPD is proposed, which allows the

measurement of the incidence positions in both direction of a 2-D FPD; along the height as well

as along the length of the FPD. This will allow rejecting by software ions at extreme positions on

the FPD and more accurate HRBS spectra can be obtained.

1.3 Swift Heavy Ion Irradiaton of HfO2/Si ultra thin film

As integrated circuit technology progress is paving the way for further miniaturization of

microelectronic components, the thickness of the gate dielectric (SiO2) in transistors decreases

to maintain capacitance at a desired level. This reduction of thickness results in high leakage

current due to quantum tunneling. In recent years, other high-k material such as HfO2 have

been used and studied for their properties as gate dielectrics. However, due to their

thermodynamic instability on Si, deposition of HfO2 on Si wafers would result in high

concentration of interface defects [17]. By introducing a thin interface layer of Silicon oxide /

nitrides between Si and HfO2 the interface quality is expected to improve [17]. Therefore it is

crucial to investigate the composition, thickness and intermixing effects to optimize the

fabrication of Hf based Metal-Oxide-Semiconductor (MOS) devices. The increase in RF-power

during sputter deposition of HfO2 on Si substrate was shown to lead to the formation of Hf-

silicates [1, 2] which belong to a new class of alternate high-k dielectric materials with tunable

electrical and thermal properties [3, 4, 5, and 6].

Swift Heavy Ion (SHI) irradiation is expected to be an important in the synthesis and

modification of many materials [18]. There are only a few reports on SHI induced mixing of

Hf/Si or HfO2/Si interfaces, even though some work has been done on ion beam studies of Hf

based high-k dielectric materials [17, 19,20]. Hence it is of paramount interest to investigate the

ion beam mixing effects of HfO2 on Si substrate, it is important to understand defect creation

and mixing at the interface due to ion irradiation. Ion irradiation effects on the material


3

properties are of great significance when HfO2 based devices for terrestrial / space application

is used.

1.4 Outline of thesis

This thesis consists of two parts. In the first part, we have the HRBS analysis of Hf based high-k dielectric

thin films while the second part consist of the SIMion simulation of 2-D splat profiles for 2-D FPD.

In chapter 2, the physical concepts of RBS and the method of simulation of RBS spectra is described. The

HRBS end station and experimental set-up in CIBA are described in chapter 3. In chapter 4, the HRBS

analysis of Hf based high-k dielectric thin films is discussed before going on to chapter 5 where the

simulation of 2-D splat profiles for 2-D FPD is looked into.

Physical Concepts Chapter 2

4

Chapter 2

Physical Concepts

Summary

RBS concept

- Kinematic factor

o Kinematic factor is defined as the ratio of the ion energy after scattering, E1 to

that before the scattering event, E0 happening on the surface of the target with a

scattering angle θ.

- Rutherford scattering cross section

o

probability at which the ion scatters at a certain angle θ

- Ion scattering cross section

o The ion scattering cross section S describes the ion stopping within the target. It

is closely dependent on the interatomic potential.

- Energy straggling

2.1 Kinematic Factor

For typical ion energies used in RBS, the mean free path between collisions are much larger

than the atomic spacing, hence all scattering events are effectively binary elastic collisions. The

dynamics of the binary collisions between two particles determine the energy of an ion after it


5

scatters from a target atom. The dynamics of binary collision can be view as a centre of mass

system where the binary collision can be modeled as a single particle moving in a central force

field potential centered about the origin of the centre of mass frame. This would eliminate the

difficulty of describing the system in the lab reference frame.

Fig. 2.1 Elastic collision diagrams as seen in the (a) lab reference frame (b) CM reference frame. Source [7]

In the lab reference frame, an incident ion with mass M1 with moving with speed ν0 and energy

E0 collides and scatters with a stationary target ion with mass M2. The incident ion then

scatters off with speed ν1, energy of E1 and scattering angle θ. The target atom scatters off with

speed ν2 , energy of E2 with angle φ. This collision can also be described using a centre of mass

system. In this system frame, the incident and the target ion approach the origin of the centre

of mass frame with speed (ν0 – νc) and νc respectively. The speed of both the incident ion and

the target ion remain unchanged after the scattering event due to the conversation of total

linear momentum of the frame.


6

M1 (ν0 – νc ) = M2 ( νc )

where

The velocity vectors of the centre of mass frame compared with the lab frame

The kinematic factor K, is defined as the ratio of energy of the ion after scattering, E1 to the

energy just before scattering, E0 where,

.

From Fig.0

Hence,

In conclusion,


7

2.2 Rutherford Scattering Cross Section

For a quantitative analysis of the RBS spectra, the probability that an ion will backscatter and be

detected by the detector at a given geometry must be known. In the previous section, the

binary elastic collision in the CM reference frame involves asymptotic values of momentum and

energy far away from the collision site. However, in this case, we have to consider the ion under

the influence of the Coulomb force as it approaches the scattering center in CM reference

frame.

The impact parameter is defined as the perpendicular distance between the target atom and

the ion trajectory in the scenario where there is no interaction between them, i.e. at infinite

distances apart. During the collision of the incoming ion and the target atom, the ion will be

deflected at an angle θc.

The total cross section σ(θc) is the cross sectional area πb2 about the target nucleus, normal to

the incident ion beam. Incident ions within these areas will be deflected with angles greater

than θc. The Angular Differential Cross-section

is defined as the probability of incident

ions scattering into angular region between θc and θc + dθc per unit solid angle Ω of the

detector, per areal density of target. Incident ions with impact parameter between b and db are

deflected through the annular area about the target. Hence

. The angular differential cross section is then

(1)


8

As noted from the equation above, the relationship between b and is needed to evaluate the

angular differential cross section. This relationship can be derived from the Classical Scattering

Integral in the CM reference frame

Where r is the distance of separation between the ion and the target atom, rmin is the distance

of closest approach, V(r) is the interaction potential and Ec is the ion energy in the CM frame.

For most case in backscattering spectroscopy, the distance of the closest approach during the

collision is smaller than the orbit of electrons, so that the interaction between the ion and the

target atoms can be described as an unscreened Coulomb repulsion of two charged nuclei with

charge of Z1e and Z2e, where Z1 and Z2 are the atomic numbers of the projectile and the target

atom and e is the magnitude of charge of an electron. The screening of the charge of the nuclei

by electrons gives an only small correction. The potential V at a distance r between the

projectile and the target atom is given in the cgs units by .

Making substitutions

and

, so that ,


9

Evaluating

, consider the CM energy at the point of closest approach,

Hence,

since at

The angular momentum has a value of at . Both quantities and are

conserved throughout the motion. Therefore,

Substituting (3) into (2)

Hence,


10

From equation (4) and (1), the Rutherford Scattering Cross section in the CM reference frame,

The Rutherford Scattering Cross section in the lab frame,

2.3 Deviation from Rutherford Scattering

In the previous section, the Rutherford Scattering Cross section is derived from the Coulomb

potential between the incident ion and the target atom. This is a good approximation when the

energy of the incident ion is sufficiently large such that it penetrates into the electron shells of

the target atom. However in small-angle scattering, low incident ion energy, the incoming ion

does no completely penetrate through the electron shells and the charge of the nucleus is

partially screened by the electrons of the inner shell of the target atoms.

This screening effect can be accounted for in the Rutherford Scattering Cross section by

introducing a correct factor . This correction factor assumes that the incoming ion gains

additional kinetic energy due to the attraction of the ion charge and the electrons of the target

atom, during the time when the ion has not penetrated fully through the electron shells. A

widely used correction is developed from Andersen et al where the potential V(r) is corrected

for the increase in kinetic energy of the ion. The correction factor was derived,


11

The correct factor is significant at large . For , approaches unity as

increase with correction of for and for .

Fig. 2.2 Plot of F ( , Ec) vs . Correction magnitude increases rapidly at small and decreases with increasing E0 at large . Source [8]

2.4 Stopping cross section

Only a small fraction of the incident ions backscatter from the target surface due to the

relatively low probability of the ions coming in close encounter with a target nucleus. Ions

which do not backscatter from the target surface proceed to travel beneath the target surface

and are backscattered at a certain depth or stop within the sample as all of their kinetic energy

is lost. As the ions travel within the target, the ions lose energy as they collide with the target

nuclei. The backscattered ions also lose energy as they travel into the target before a

backscattering event as well as out of the target after a backscattering even. Hence, energy loss

of the backscattered ion is larger as the depth of the backscattering target beneath the surface

increases. This measure of energy loss provides information of the elemental profile as well as

the depth profile of the elements in the target sample.


12

Stopping cross-section is used to discuss on the energy loss. The stopping cross section is

where N is the atomic density and is the energy loss per unit path length

within the target. The stopping cross-section can be contributed by two components, the

stopping cross-section due to collision with nuclei and electrons, Sn and Se respectively. Nuclear

stopping are due to elastic collisions that can give rise to large scattering angles and discrete

energy losses of the ion per collision event, while electronic stopping are mainly due to inelastic

collisions involving much smaller energy losses per collision as well as negligible angular

deflection of the ion trajectory. At higher ion energies, only Se is significant as Sn is non-

negligible at energy, E ≤10 keV/amu. Since in RBS or HRBS, measurements are usually done with

He+ ions with incident energy, E0 ≥ 500 keV and the energy of the backscattered ion, E1 ≥ 250

keV, nuclear stopping is negligible.

There are theoretical models to describe electronic stopping at both low (E ≤30 keV/amu) and

high (E ≥1 MeV/amu) ion energies. However, most RBS measurements are carried out an

intermediate ion energy range. For He ions, there are two commonly used functions to describe

the ion's stopping cross-section, the Ander-Ziegler stopping data and the Ziegler Biersack

stopping data, where different function are used to fit the Stopping cross-section for high and

low ion energies, Shigh and Slow.

The Andersen-Ziegler stopping for He is

and

where A1 to A5 are tabulated parameters. The Zierler-Biersack stopping for hydrogen stopping

data is

and


13

where C1 to C8 are fitted parameters. The stopping cross-sections are then scaled using

effective charge γHe2,

where

2.5 Energy Straggling Light particles such as H or He lose energy due to the statistical fluctuations in the electronic

and nuclear energy processes as they travel within the target sample. These statistical

fluctuations causes a broadening of the ion energy distribution which is known as energy loss

straggling. The distribution of energy loss ΔE for the particles after passing through a foil gives a

distribution that is approximately Gaussian when ΔE is small compared with the incident energy

E0. Thus the probability of finding an energy loss between ΔE and ΔE + dΔE is expressed as

where is the mean energy loss and is the variance if electronic energy. Based on

classical considerations of collisions between a charged particle such as proton or α particle and

free target electrons, is given as

where is the path length in the target sample. This expression is also referred to as the

Bohr's value of energy loss straggling. Bohr's straggling theory is valid when ion velocity is high,

where the straggling value is almost independent of ion energy. For lower ion energy E, Chu's

straggling theory can be used,


14

where H is the Chu correction factors, which are tabulated for 100 ≤ E/M1 ≤ 1000 (keV/amu) by

Szilágyi [9] are plotted for several values of E/M1 as a function of Z2 in Figure 2.3. For 500 keV

He ions, the deviation from Bohr's straggling is around 60% to 80%.

Fig. 2.3 Plot of Chu correction factors H vs Z2 for various E/M1 values. Dots are original data from Chu and the lines are extrapolations by Szilágyi [9]. Source [7]

Ions with different charge states will also transfer different amounts of energy to electrons

during a backscattering event. For He ions, the charge state varies as they travel within the

target sample due to the excitation and capture of electrons within the target sample. These

fluctuations in charge state contributes to additional energy straggling effects and be described

by a semi-empirical formula with fitted parameters C1 to C4

where and


15

For 500 keV He ions, the additional energy straggling factor

is estimated to be around

0.25. The total energy straggling is the sum of Chu and Yang straggling components,

2.6 Rutherford Backscattering Spectrometry

The various quantities describe earlier are now used to provide a picture of RBS analysis of thin

film on a substrate which is one of the focus of this thesis. In a RBS measurement, the incident

ions of energy E0 is backscattered with a scattering angle θ with energy E1 and its detected by a

detector placed at certain position along the ion trajectory. A spectrum of the distribution of

the energies E1 of the backscattered ions is then obtained which is used to determined the

elemental composition of the target using numerical simulations of the energy spectra with the

software package SIMNRA.

Fig. 2.4 Diagram of RBS measurement


16

2.7 Ion Channeling

Ions incident onto a target with a lattice structure along a major crystalline axis may be steered

into channels (i.e. “channeled”) where they undergo a series of correlated, small angle

collisions with the nuclei that line the channels.

Fig. 2.5 Schematic of ion channeling. Source: [10]

The incident ions will be deflected by the first atom on the surface atomic layer, forming a

“shadow cone” which shields the rest of the atoms lining the channel from head-on and close-

encounter (low impact factor) approach by the ions (Fig. 6.5(a)).Subsequent encounters of

channeled ions with lattice atoms will be small-angled collisions with large impact factors, with

the ion trajectory exhibiting oscillatory behavior within the channel (Fig. 6.5(b)) in near-surface

regions. The backscattering cross-section of channeled ions are therefore greatly reduced, the

RBS signal from the crystalline (Si) substrate may fall by up to 98% of the random yield for pure

crystals with clean surfaces along major axes.


17

Fig. 2.6 (a) Schematic of the formation of the shadow cone at the surface and the trajectories of channeled particles. The horizontal scale on the right is compressed in relation to the vertical scale to show the trajectory oscillations. (b) The comparison between the channeled and the non-aligned RBS spectrum. The channeled spectrum shows a drastically reduced substrate signal. Source [10]

2.8 Thin film on substrate In this thesis, the focus on the thin film deposited on a substrate is focused on depth profiling

and stoichometry of elements in the thin oxide film at the interface region of the sample.

Fig. 2.7 (a) Scattering geometry and (b) spectrum of an RBS measurement of a thin compound target.

Source [11]


18

Fig. 2.7 illustrates the scattering trajectory and the RBS spectrum of a thin film AyB1-y on a thick

substrate S. In high k gate dielectric, A is usually a heavy element, B is either O or N, and S is

usually Si. The signals from elements A and B in the spectrum have high energy edges at KAE0

and KBE0 respectively. The substrate signal S pushed back to lower energy by ΔEs, due to the

ions losing energy within the thin film. The signal from B rests on top of the substrate signal S,

due to KBE0 < KSE0 − ΔEs. Ions will lose the same amount of energy per unit length along the way

in, but may lose a different amount along the way out depending on which atom they

backscatter from, due to the difference in K values. The energy widths of the respective signals

in the spectrum are:

and

where

and

, is the areal density of the thin film, is the stopping cross section of the ion as in

enters the sample while and

is the stopping cross section of the ion as after it

backscatters from ion A and B.

Apply the Bragg's rule of additivity which states that the stopping cross section of the

compound can be estimated by the linear combination of the stopping cross section of the

individual atoms

The area of the spectrum attributed to element A and B are


19

Using the areas, the stochiometric ration of the two elements A and B can be determined.

2.9 SIMNRA Numerical Simulation of RBS spectrum SIMNRA is a computer software that carries out numerical simulations of an RBS spectrum. In

the numerical simulation by dividing the target sample into i thin sub-layers as shown below in

figure 2.8. Each sub-layers is thin enough such that the variation of the stopping cross section is

assumed to be negligible within each layer. In the ith sublayer the energy of the ion that enters

the layer of thickness δx is Ei-1 and the energy the ion that exits the layer is Ei.

Fig. 2.8 Diagram of the target divided into thin layers. Source [11]

The energy loss within the layer i is ΔE and the mean energy of the ion in layer i is the incident

ion energy E0 subtracting the energy loss within layer 1 to layer i-1 and half the energy loss

within layer i which are given by


20

The integral in is numerically computed using the Runge-Kutta method. The ion energy

along the outward is computed in the same way, using for the backscattering at the back

of layer i.

Beam straggling within the ith layer for the inward is calculated using

where the first term in the equation above is the non-statistical beam straggling due to varying

stopping cross-section and is the total (Chu and Yang) energy straggling within layer i.

Scattering from within each layer will result in a signal in the spectrum called the "brick". Each

brick has an area

The stopping cross-section is evaluated at the mean energy in the layer and is assumed to

be constant. The final simulated spectrum is formed by the summation of the "bricks" from

different elements and different depths (layers).

HRBS Set-up Chapter 3

21

Chapter 3

HRBS Set-up

3.1 HRBS Endstation

The HRBS end station was fabricated by the Machinery Company of Kobe Steel Ltd and installed

at CIBA in 2003. The general setup consists of a Main chamber with a load lock chamber, Ultra-

high Vacuum (UHV) system (pumps, valves and interlocks), 5-axis Goniometer, Spectrometer

magnet and Micro-Channel Plate – Focal Plane Detector stack (MCP-FPD)

Both the main and the MCP-FPD chambers are constantly maintained under UHV with two

turbo-molecular pumps, which are located beneath the main chamber and the MCP-FPD

chamber. Sample exchange is carried out by a transfer rod which transfers a target holder onto

the goniometer attachment in the main chamber from a load-lock chamber through a gate

valve. A controller program in the control cabinet oversees the vacuum interlocks system. This

allows for programmed or manual control of all valves as well as the goniometer rotation axes.

During measurements, the divergence of the ion beam is defined using the motorized slits

located ~ 1 m before the main chamber. Backscattered ions from the sample target enter the

detection system, which consists of a spectrometer magnet and a Micro-Channel Plate – Focal

Plane Detector (MCP-FPD) stack. The output signal from the FPD is then processed by a system

of electronics in the control cabinet to provide information of the position of incidence along

the length of the FPD. The output spectrum is sorted by a MCA before the final spectrum is

obtained in the computer


22

3.1.1 Main chamber, load lock and vacuum system

The sample is placed in a specially designed sample holder which is held on the goniometer

attachment in the main chamber during RBS measurements. Insertion and removal of the

sample holder is carried out using a transfer rod within the load lock chamber.

Fig. 3.1 (a) Main chamber, goniometer and load lock. (b) Load lock with a sample holder (c) View of sample holder on the goniometer in the main chamber through the main viewport. Source [11]

A UHV vacuum of smaller than 5 ᵡ109 mbar is maintained by a Mitsubishi FT-800WH turbo-

molecular pump (TMP) in main chamber (TMP 1) and a Mitsubishi PT-50 TMP in the MCP-FPD

chamber (TMP 2).

Both TMPs are being backed by a Mitsubishi DS-251L scroll pump with valve V2 perpetually

open. Valve V3 allows the load-lock to be pumped (also by the scroll pump), V4 controls the

venting with N2 during sample change and V1 isolates the load lock from the main chamber.


23

The network of valve is monitored by an interlocks system at the control cabinet which

prevents sudden change in vacuum pressure due to accidental activation of valves.

Fig. 3.2 Schematic of the vacuum pump and valve network. Source[11]

During sample change, the interface from control cabinet activates sequential steps which

activates the appropriate valves. During insertion of the sample into the main chamber, the

sample holder is placed on the transfer rod within the load lock with the all valves except V2

closed. V3 is opened to allow the load lock to be pumped to a pressure of ~ 10-2 mbar, after

which V1 is opened to allow the sample to be transfer into the main chamber. Lastly the

inserting rod is retracted into the load lock and both V1 and V3 are closed. On the other hand,

in sample removal, V3 is first open to pump the load lock down before V1 is opened. After the

sample is removed and the transfer rod id retracted into the load lock, V1 and V3 are closed.

Finally, V4 is opened to allow N2 to flood the load lock back to atmospheric pressure and the

load lock chamber can be opened to remove the sample.


24

3.1.2 Goniometer

A Kitano Seiki 5-axis goniometer controls the sample orientation in the main chamber by

enabling translation in the x, y and z axes, as well as rotation about the θ and ϕ axes. The

translation resolution is 0.01 mm with a repeatability of ≤ 0.05 mm along all directions, while

rotations have resolution of 0.05° and are repeatable to within ± 0.05. An electric potential of ~

+480 V is applied to the attachment which holds the sample holder during measurements,

suppressing secondary electron emissions to allow for accurate beam current readings.

Fig. 3.3 Schematic of the HRBS goniometer. Source: [12]


25

3.1.3 Micro-channel Plates

The 2-D FPD is used to detect the position of the backscattered ions along its length and

breadth. The position is then analyzed to determine the energy of the corresponding

backscattered ions. However, the charge of the backscattered ion is too small to result in an

electrical pulse significant enough to be processed by the electronic equipment. With the

implementation of the MCP, the electrical signal by the backscattered ion can be amplified by

an electron multiplication process through the channel plates. The walls of the plate have a low

electron emission work function and a voltage bias of 1kV is applied across each channel plate

using an ORTEC 660 High Voltage Bias. This would cause the incident backscattered ion to

initiate an electron cascade down the channel plate. The electron multiplication process will

saturate and an electrical pulse would be recorded.

There are residual gases in the channels which might be ionized during the cascade process

which will accelerate upwards within the channel. This ionized gas will gain kinetic energy as it

accelerates upwards and might initiate another cascade, creating dark counts. The orientation

of the plates at an angle relative to each other prevents this initiation by ensuring that the gas

ions at the bottom stack will be stopped at the junction between the two plates.

Fig. 3.4 Diagram of Micro-channel plates


26

3.2 Electrostatic plates

Work has been done by C. S. Ho [22] to install a pair of electrostatic plates as shown in figure

3.5 between the spectrometer magnet and the MCP chamber.

Fig. 3.5 Schematic and layout of the installation of the electrostatic plates. Source [11]

The plates were carefully adjusted to be horizontal, so that all ions are deflected only in the vertical

direction. The electrostatic field serves to eliminate low-energy stray ions that have scattered off the

collimator, floor, walls or ceiling of the conduit along any part of the ion trajectory between the target

and the MCP. Without the electrostatic plates, the low-energy stray ions will produce a background

counts in the actual HRBS spectra. The addition of the electrostatic plates would then remove a large

part of the background counts and increasing the accuracy of the HRBS measurement.


27

3.3 1-D Focal Plane Detector and HRBS electronics

The FPD is a 100 mm long resistive strip of uniform resistance per unit length. As the electron

cascade from the MCP deposits a charge pulse on the FPD, the position of the charged pulse

can be determined by a system of electronics. A charged pulse detected on point X, would

cause a current flowing to the right and to the left of the FPD, IL and IR respectively. The charged

collected on the left and right of the FPD, QL and QR are measured over a time interval ∆t and

compared to the total charge collected to determined distance X from the edges of the FPD.

The length of the FPD is Land since the FPD has uniform resistance per unit length, we have

Fig. 3.6 Schematic of 1-D Focal Plane Detector and HRBS electronics. Source[11]


28

The charge division to determine the position of the electron cascade is calculated by a system

of analog processors. The charge pulses QL and QR are each processed first by ORTEC 113 Pre-

amplifier and then by ORTEC 571 Amplifier [11]. The resultant pulses were then added using

ORTEC 533 Dual Sum and Invert card while the Seiko EG&G PSDA card is used to divide an

amplified signal with the summed signal to obtain the position output [11]. The summed signal

output is also processed. The output is then processed by a Canberra 8706 ADC which is

subsequently sorted using a Labo NT2400 Multichannel Analyzer and finally displayed on the

PC[11].

3.3.1 2-D Focal Plane Detector

For a 2-D FPD, there are added long resistive strips of uniform resistance in another dimension.

Similar to the 1-D system, the electron cascade from the MCP deposits a charge pulse on the

FPD, the 2-D position of the charged pulse can be determined. A charged pulse detected on

point X in the x-direction and point Y in the y-direction, would cause a current flowing to the

right and to the left of the FPD, IL and IR respectively as well as to the top and the bottom of the

FPD, IT and IB respectively. Similar to the charged collected on the left and right of the FPD, QL

and QR, the charged collected at the top and bottom of the FPD QT and QB are measured over a

time interval ∆t and compared to the total charge collected to determined distance Y from the

top and bottom edges of the FPD. With height, H of the FPD and taking account the uniform

resistance per unit length of the FPD, we have

With the knowledge of the x and y positions of the incident charge pulse, the 2-D position of

the incident charge pulse can be determined.

Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon

Chapter 4

29

Chapter 4

Study of Swift Heavy Ion Irradiation effects on Hafnium based high k-

dielectric thin films deposited on Silicon

4.1 Swift Heavy Ion

The energetic ions through a material loose energy via two processes along their trajectories.

The two processes are known as nuclear energy loss and electronic energy loss. In nuclear

energy loss process, dominant in low energies, the energy is lost by elastic collisions of incident

ions with the atoms in the material. However at dominant at high ion energies (>1

MeV/nucleon), electronic energy loss is dominant. In electronic energy loss process, the energy

is lost by inelastic collisions of the ion with the electrons of the atoms, leading to excitation or

ionisation of the atoms. At such high energies, the velocity of the ion is comparable to or higher

than the velocity of Bohr electron. Heavy ions with such high energies are also referred to as

Swift Heavy Ions (SHI).

4.2 Ion beam Mixing

Ion beam mixing (IBM) is a process, in which the atoms of two different species across an

interface are mingled together under the influence of the passage of ion beam. Conventionally

it is achieved by low energy ion up to a few MeV[12]. In IBM, elastic collisions and subsequent

collision cascades, recoil implantation and radiation-enhanced diffusion is observed. Collision

cascade is initiated only in the case when the recoils have sufficient energy to displace the


Chapter 4

30

lattice atoms. The heavier ions will have large number of collision cascades as compared to that

of lighter ions. IBM was considered to be a phenomenon associated with low energy ion

irradiation. However since early 1990s, the ion beam mixing by SHI irradiation was observed.

In all the above studies, SHI induced mixing at the interface has been identified as diffusion in

melt phase created by transient temperature spike [13,14]. It is proposed that each ion

produces a transient molten cylindrical zone in the material for typical time duration in the

regime of picoseconds. The inter-diffusion across the interface takes place during the molten

phase resulting in mixing. Quantitatively, it has been shown that the diffusivity of the atomic

species across the interface during the transient melt phase as obtained in these experiments

[13,14], is of the order of 10-6 to 10-9 m2s-1. Such a high diffusivity is possible only for the liquids,

which supports the hypothesis that the ion beam mixing is a consequence of inter-diffusion

across the interface during transient melt phase.

4.3 HfO2/SiO2/Si Samples

HRBS analysis was done for four HfO2/SiO2/Si samples obtained from SEMATECH, USA which

were grown by Atomic Layer Deposition (ALD). The sample in the absence of Swift Heavy Ion

Irradiation is labeled as Pristine-H1A where its sample structure is shown in figure 4.1. The

other three samples are irradiated at IUAC, New Delhi using 120 MeV Au ions with different

fluence and labeled as H1B, H1C and H1D. The four samples are described below:

i) Pristine-H1A

ii) 1E13 ions/cm2 120 MeV Au irradiated-H1B

iii) 5E13 ions/cm2 120 MeV Au irradiated-H1C

iv) 1E14 ions/cm2 120 MeV Au irradiated-H1D


Chapter 4

31

Fig. 4.1 Sample structure of Pristine-H1A

4.4 HRBS experimental parameters

The samples were measured using a 500 keV He+ beam incident on the sample and ions

scattered at 65° with incident and exit angle 54.7° and 60.3° respectively. The backscattered

ions were then analyzed by the spectrometer and were collected by the MCP-FPD. Two

experimental data for each sample is obtained. The first data obtained is the aligned HRBS

spectra (along <111> axis of Si) in order to minimize background scattering from Si and analyze

amorphous layers (SiO2/HfO2) on Si surface. Prominent surface peaks corresponding to Si and

O from amorphous layers on surface are observed due to a reduction of about 80% in the back

scattering yield of Si (χmin = ~ 20%) in <111> aligned spectrum. A non-aligned or random HRBS

spectrum is also obtained where angle φ is slightly rotated under IBM geometry which was then

simulated using SIMNRA to obtain an elemental depth profile.

4.5 HRBS Depth profiling results

The non-aligned and channeled spectra of all four (H1A, H1B, H1C, H1D) samples are shown the

figures 4.2 to 4.5:


Chapter 4

32

Fig. 4.2 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation of Pristine-H1A sample

Fig. 4.3 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1B-1E13 Au sample


Chapter 4

33

Fig. 4.4 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-5E13 Au sample

Fig. 4.5 Aligned (Channeled), Non-aligned (Random) HRBS spectra and SIMNRA simulation H1C-1E14 Au sample


Chapter 4

34

In figure 4.5 below, an overlay of Hf peaks from the previous four graphs for is illustrated. A

widening of the Hf peaks as the irradiation fluence increase from sample H1A to H1D. This

supports the proposition that ion beam mixing is present which results in the inter-diffusion of

Hf into the sample and that the increase in fluence of Au ion irradiation corresponds to an

increase in the degree of inter-diffusion of Hf into the sample.

Fig. 4.6 Aligned (Channeled) HRBS spectra of Hafnium peak for all four samples (H1A, H1B, H1C, H1D)


Chapter 4

35

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50

Co

nce

ntr

atio

n

Depth ( 1015 atoms/cm2)

H1A (Pristine)

Hf

Si

O

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Co

nce

ntr

atio

n


H1D (1E14 Au)

Hf

Si

O

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50 55 60

Co

nce

ntr

atio

n


H1C (5E13 Au)Hf

Si

O

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45 50

Co

nce

ntr

atio

n


H1B (1E13 Au)

Hf

Si

O

Fig. 4.7 Elemental depth profile for H1A, H1B, H1C, H1D

Using SIMNRA, the concentration of the Si, O, Hf in various depth layers is simulated. A total of

five different depth layers are fitted to the non-aligned spectra of each of the four samples. The

top layer of all four samples consists of HfO where the stoichiometric ratio of Hf : O for all four

samples is roughly 1 : 2. The subsequent interface layers consist of a HfSiO layer and three

different SiO layers with different stoichiometric ratios. The bottom layer is the Si substrate

which is for clarity reasons, not depicted in figure 4.7. As observed from figure 4.7, there is a

systematic increase in the thickness of the interface layers as the irradiation fluence increase

from sample H1A to H1D (thickness of interface layers for H1A ~ 25 × 1015 atoms/cm2, H1B ~

26.5 × 1015 atoms/cm2 , H1C ~ 31 × 1015 atoms/cm2 , H1C ~ 38 × 1015 atoms/cm2).


Chapter 4

36

4.6 Conclusion

HRBS measurements suggest that the interlayer is a mixed HfSiO/SiO layer instead of a pure

SiO2 layer as intended. It is well known that SiO2 is very much stable on Si surface. Hence this

mixed layer might have formed either during or after the deposition of HfO2 layer. Inter

diffusion of Hf into SiO2 and Si into HfO2 at SiO2/HfO2 interface is likely to be responsible for the

observed mixed layer. An interdiffusion of O into the Si substrate. This information is expected

to be useful for understanding the kinetics of growth during atomic layer deposition.

A systematic increase in thickness of the interlayer as a function of increasing fluence is also

observed as seen in figure 4.7. These observations confirm that SHI using high energy Au atoms

can induce ion beam mixing where inter-diffusion of Hf and O across HfSiO/HfO2 interface is

observed. Such inter-diffusion is also more pronounced as irradiation fluence increases.

Simulation and characterization of new 2-D focal plane detector using SIMion

Chapter 5

37

Chapter 5

Simulation and characterisation of new 2-D focal plane detector using

SIMion

5.1 2-D Focal Plane Detector

Fig 5.1 Diagram of 2-D FPD with true counts (red dotted ovals) and counts derived from HRBS (black

ovals)

A 2-D FPD allows the profiling of splat profiles of the end of the ion trajectories in both

directions of the FPD; along the height as well as length of the FPD. If the true counts, the red

dotted oval seen in figure 5.1 is known, the dark counts can be discerned from the original

experimental data or the black ovals as seen in figure 5.1. Hence, any counts that originate from

the shaded area seen in figure 5.1 would be considered as dark counts and can be screened out

to obtain a more accurate HRBS spectrum. It is also important to characterize the height as well

as the width of the splat profiles to determine whether the dimensions of the splat profile

would fit well into the 2-D FPD.


Chapter 5

38

In this part of the thesis, we look into the 2 dimensional splat profile onto the median (x-y)

plane along the FPD of the exit beam. Since the FPD determines the energy of ion according to

ion's position along the length of the FPD. A simulation is performed using SIMION to sweep the

ion incidence position across the length of FPD. The length and height of the FPD is

approximately 100mm and 15mm respectively. The 2-D splat profile (height and width) of the

ions of different energies at the end of their trajectories incident on the FPD is characterized

and then investigated. An example of simulation is shown in figure 5.2 as a point ion spot is

created at S and its trajectory is simulated through a circular collimeter (1mm or 2mm in

diameter) and a subsequent splat profile is obtained at the end of its trajectory.

Fig. 5.2 Schematic of simulation done using SIMion


Chapter 5

39

5.2 Overall layout of the HRBS detection system

Fig 5.3 Schematic of Spectrometer magnet, MCP-FPD in HRBS. Source [11]

In CIBA, HRBS spectrometer magnet used in a double-focusing 90° sector magnet with a straight

edge rotated by 26.6° and a circular exit edge with radius 0.12569m as shown in the diagram in

figure 5.3. Assuming a static magnetic field, every ion energy, E has a unique “central

trajectory” with radius r given by:


Chapter 5

40

where m = Mass of the ion , B = Magnetic flux density and q = Ion charge.

A 90° sector magnet of radius r0 with flat entrance and exit edges that are both rotated at 26.6°

is expected to produce a stigmatic image of a point source at both object and image distances

of 2r0 = 0.350m. The HRBS spectrometer and detection setup is designed to produce a stigmatic

image according to this principle. As seen from the diagram from figure 5.3, the incident beam

backscatters from the sample at S, passes through the collimeter which defines the beam

divergence before entering the magnet at P, When the ions travels along a trajectory of radius

of r0= 0.175 m, they will exit the spectrometer magnet at Q before they ending up at the MCP-

FPD stack at Q. Assumptions were made that no fringe fields were present in the spectrometer

magnet.

5.3 Spectrometer ion optics

5.3.1 Beam entry parameters

In the SIMION simulation, the ion beam was assumed to have incident on a target tilted at 45°

with IBM geometry (Fig. 4.4). The incident finite beam spot size on the target is 1 × 1 mm as

seen along the target normal. Particles backscattered at a scattering angle of α° will form a

beam of half--width, ω = 0.5 × 10-3 sin β° (metres) that will subsequently be collimated by a 2

mm or 1mm circular collimeter placed between the target in the scattering chamber and the

magnet entrance. The simulation was repeated thrice with scattering angle α° at 90°, 110° and

130° with corresponding β° at 45°, 65° and 85° respectively. A point beam spot is also simulated

as a reference to the finite beam spot.


Chapter 5

41

Fig 5.4 Schematic of the incident and backscattered beam profiles

Fig. 5.5 Finite backscattered beam profile and point source approximation

As seen in figure 4.5, the total distance between the beam spot on the target and the magnet

entrance is 0.350 m, and the collimator is 0.165 m from the magnet entrance. The maximum

divergence of the backscattered beam through the collimeter can be modeled by the beam

envelopes created by the ion trajectories at the extreme ends of the beam spot. The

combination of the beam envelopes point source at point S' at a distance d would model the


Chapter 5

42

maximum divergence envelope of angle θ0 (red dotted lines in figure 5.5) of the beam spot that

contain all envelopes formed by the finite incident beam. The point beam at S' was therefore

used as an equivalent of the finite beam. By similar triangles, we have

Hence, for a 90°, 110° and 130° scattering angle, d is 295 mm, 292 mm and 288 mm

respectively.

5.3.2 Drawing the magnet

The program simulates a 3-dimensional universe called workbench that is divided into grids.

The centre of each grid cube is known as a grid point, while the separation between 2 adjacent

grid points is known as a grid unit. Grid points are divided into 2 types: electrode points and

non-electrode points. The size of the workbench was first defined, followed by the drawing out

of the exact shape of the magnetic pole pieces (known as electrodes within SIMION). Drawing a

pole piece is done by deciding the set of grid points to be defined as electrode points, while the

rest of the grid points are designated to be non-electrode points.

The exact shape of the HRBS spectrometer magnet was drawn using a geometry file where

exact geometrical shapes were drawn using its in-built definition language by TK Chan [11]. The

pole pieces were separated by 18 mm, while their thicknesses were drawn out to be 40 mm.

The exact thickness along the z-direction was not simulated because only the shape and the

magnetic potential at their boundaries define the magnetic field between them. The inner

boundary edges are filed at an angle of 45° at both the magnet entrance and exit.


Chapter 5

43

Fig. 5.6 3-D isometric view of the workbench with a magnified view of the spectrometer magnet. Source [11]

5.3.3 Maxwell’s and Laplace’s equations The Maxwell’s equations for electric and magnetic fields in vacuum for static magnetic fields

not containing any electric charges:

Since both curls and divergence are zero, we can write the Laplace's equation in terms of the

scalar potential where and


Chapter 5

44

However, since only magnetic field is involved in our set-up, the subscripts are dropped and the

scalar potential now refers the scalar magnetic potentials.

5.3.4 Refining the magnet array All electrode points within a single magnetic pole piece share the same magnetic potential. A

non-zero potential was chosen for the top magnetic pole piece and a zero potential is chosen

for the bottom magnetic pole piece. All non-electrode points are set to zero potential. The

electrode potentials form the Dirchlet boundary condition which ensures the uniqueness of the

harmonic solutions to Laplace’s equation.

5.3.5 Finite Difference Method

The next step was to solve the Laplace’s equation numerically to determine the magnetic

potentials for all non-electrode points within the workbench that will reflect the correct

magnetic field, this is known as “refining the array” in SIMION. SIMION solves the Laplace

equation using the numerical method called the “Finite Difference Method (FDM)" which is

rather straightforward which is essentially a process of assigning a potential to each non-

electrode point that is equal to the average value among those of the neighbouring points.

SIMION does this sequentially and over a number of iterations. During each iteration, the

program sequentially calculates for every non-electrode point within the array the average

potential of the 6 neighboring points (Figure 5.7). A potential distribution is then obtained after

the iterations are completed (Figure 5.8). This also implies that the potential energy map from a

static electric field can contain no local minimum or maximum.


Chapter 5

45

Fig. 5.7 Diagram depicting “Finite Difference Method (FDM)"

Fig. 5.8 The potential distribution plot along the x-y plane at a fixed value of z. The darkened flat top represents the region with uniform magnetic field, while the smooth slopes at the sides represent the non-uniform fringe fields. Source [11]

5.3.6 Calculation of ion trajectories Ions of mass M were created at point S and given an initial energy E. The program divides the

flight duration of the ion through into time steps in which the size of the time steps is

dependent on the rate of change of magnetic potential gradient at that point. At regions of


Chapter 5

46

constant gradients, the time steps are larger as compared to the regions with greater gradient

variations. At each time step, the program also employ linear interpolation between the

potential V at the ion's position with the potentials at 6 adjacent grid points, Vi (i = 1,2,3,4,5,6)

to determine the potentials at the surrounding 6 intermediate points half a grid unit (gu) from

the current ion position which is half the addition of the V and Vi. These potentials were then

used to obtain the component of the magnetic field as well as the acceleration in the x, y and z

direction using to B = − . The acceleration components derived from

, which leads

to the components in the velocity change during every time step:


Chapter 5

47

5.4 SIMion simulation details

Fig. 5.9 The overview of the workbench in the x-y plane looking down towards the negative z-direction. Source [11]

He+ ion spot with a finite width were created at point S' and given an initial energy E. The ion

then follows a trajectory as determined by the spectrometer magnet with a fixed magnetic field

between the pole pieces. The half-width of the beam spots 0.42mm, 0.45mm and 0.5mm

which simulates the ion backscattering at different scattering angles (90°, 110° and 130°

scattering angle are respectively). Ions of different backscattered energy were then created at

point S' to sweep the ion incidence position across the FPD of length approximately 100mm. A

point He+ ion spot was also created to contrast the splat profile for the finite beam spot.

d


Chapter 5

48

5.5 SIMion simulation results

5.5.1 Splat profiles

Fig. 5.10 Splat profile for a point spot and beam spot of E = 427keV collimated by a 1mm collimeter

For each ion energy and beam spot size, we obtained a splat profile at the end of its trajectory

at the FPD. Here, a new parameter is defined, ε which is ratio of the E to E0 where E is the fixed

energy of the backscattered ion incident on a fixed position on the FPD, while E0 is the energy

of the backscattered ion at which the end trajectory is incident on the centre of the FPD. The

splat profile of ions with energy, E from 400 keV to 571 keV (range of ion energy to sweep the

ion incidence position across the FPD of length) was plotted out and studied. An example of a


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49

plotted splat profile is illustrated in figure 5.10 which depicts the splat profile for a point spot of

as well as a beam spot of half-width 0.42mm of E = 427keV collimated by a 1mm collimeter.

In figure 5.11, the various splat profiles corresponding to different energy, E (400 keV to 421

keV) for a point spot simulated through 1mm collimeter are plotted out. It can be observed that

the height of the splat profiles (dimension of the splat profile in the z-position) decreases as

energy of the point spot increases from 400 keV to 421 keV.

Fig. 5.11 Splat profiles of a point spot of energy, E from 400 keV to 421 keV simulated through 1mm collimeter

However, as the energy of the point spot, E continues to increase from 421 keV to 442 keV, the

height of the splat profile increases (figure 5.12). The point at which the splat profile is


Chapter 5

50

minimum can be deduced to be double focusing point of the spectrometer magnet which is at ε

≈ 0.87, at the right end of the FPD. Hence, it can be seen that the height of the splat profile

increases as the end trajectory incident the FPD moves to the left of the FPD. The splat profiles

for the point spot through a 2mm collimeter were also plotted out (see figure A.1 and A.2) and

the splat profiles follow the same trend as that of the 1mm collimeter.

Fig. 5.12 Splat profiles of a point spot of energy, E from 421 keV to 442 keV collimated by 1mm collimeter

5.5.2 Height and Width of splat profiles


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51

In figure 5.11 and 5.12, the height variation of the splat profile along the length of the FPD is

observed. However, the width variation is too small to be observed. Hence, an overall height

and width of the splat profile along the FPD is plotted out for point spot and various beam spot

sizes collimated by 2mm collimeter (figure 5.13 and figure 5.14). As depicted in figure 5.13, the

height of the splat profiles decreases as ε increases until it reaches a minimum point at the

double focusing point after which it continues to increase. The height of the splat profiles are

shown to be all smaller than 8mm. The height of the splat profile along the FPD through a 1mm

collimeter was also plotted out (see figure A.3) and the splat profiles follow the same trend as

that of the 2mm collimeter. The height of the splat profiles for that of a 1mm collimeter are

smaller than 4mm.

Fig. 5.13 Height of the splat profiles for point and beam spots collimated by 2mm collimeter


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52

As depicted in figure 5.14, the width of the splat profiles for the beam spots increases as ε

increases. However, for the point spot, the width of the splat profiles decreases until it reaches

a minimum point before it starts to increase. The trend for the beam spot is expected to follow

the trend of the point spot as ε continues to decrease. The width of the splat profiles are shown

to be all smaller than 2mm. The width of the splat profile along the FPD through a 1mm

collimeter was also plotted out (see figure A.4) and the splat profiles follow the same trend as

that of the 2mm collimeter. The height of the splat profiles for that of a 1mm collimeter are

smaller than 1mm.

Fig. 5.14 Width of the splat profiles for point and beam spots collimated by 2mm collimeter

5.5.3 Variations in starting x-position of backscattered ions


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53

The starting position of the point spot was varied in the x-direction from the original position at

675 grid unit (gu) on SIMion workbench and the corresponding height, width as well as the

centre position variation of the splat profile at double focusing point was then studied. This was

to model for the position uncertainty in the x-direction of the backscattered ion in HRBS. Here,

674 gu is 1mm in the x-direction closer to the spectrometer magnet and 676 gu is 1mm in the x-

direction further from the spectrometer magnet. In figure 5.15, 5.16 and 5.17, the height, width

and centre position of the splat profile at double focusing point with different starting points of

the backscattered ion trajectory , collimated by a 2mm collimeter are plotted out respectively.

Fig. 5.15 Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)


Chapter 5

54

Fig. 5.16 Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)

Fig. 5.17 Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (2mm collimeter)


Chapter 5

55

The variations of height of the splat profile due to variations in starting x-position of

backscattered ions is around 0.01mm and variation of width is around 0.015mm which is also

the height and width resolution at double focusing point for a starting position uncertainty of

1mm. The variation of the centre position of the splat profile at double focusing point is smaller

than 0.0015mm, which is relatively quite small. For 1mm collimeter, see figures A.6, A.7 and

A.8, the corresponding variations of height and width is around 0.003mm and 0.007mm

respectively. The variation of the centre position is smaller than 0.0005mm which is also

relatively quite minute.

5.6 Simulation Conclusion

A SIMION Simulation of height and width of the Splat profile of beam spot of different

scattering angle and different half width for different backscattered ion energy was done. For a

2-D focal plane detector, it important to consider of height of the splat profile; if the height of

the splat profile is larger than the height of the detector, some of the counts will not be

recorded which would distort the HRBS spectra. The 2-D FPD that is available has a height of 15

mm and length of 100 mm. The simulations shows that height of splat profiles for 2mm

collimeter is below 8mm and for 1mm collimeter, it is below 4mm. Hence, we can safely

assume that the splat profiles will fit into the height of the 2-D FPD and all the counts on the

FPD can be recorded. The width of the splat profiles for 2mm collimeter is smaller than 2mm

while that of the 1mm collimeter is smaller than 1mm. Hence, it can deduced that at least 50

splat profiles of 50 different ion energies (2mm collimeter) or at least 100 splat profiles of 100

different ion energies (1mm collimeter) can be fitted into the length of the FPD.

The height and width resolution at double focusing point for variations in starting x-position of

backscattered ions of uncertainty of 1mm through a 2mm collimeter is around 0.01mm and


Chapter 5

56

variation of width is around 0.015mm. The corresponding height and width resolution for 1mm

collimeter is around .003mm and 0.007mm respectively.

The variation of the centre position of the splat profile at double focusing point is relatively

quite small. Hence, the uncertainty of the starting position does not cause a large variation of

the position of the double focusing point of the FPD.

Bibliography

57

Bibliography

[1] W. J. Zhu, T. P. Ma, S. Zafar, and T. Tamagawa, IEEE Electron Device Lett., 23, (2002), 597.

[2] A. Y. Kang, P. M. Lenahan, and J. F. Conley, Jr., IEEE Trans. Nucl. Sci., 49, (2002) 2636.

[3] S. K. Dixit, Ph.D. Thesis, Vanderbilt University, Nashville, TN, USA, May (2008) and refs. therein.

[4] L. Pereira, Mat. Sci. and Engg. B, 109, (2004) 89.

[5] H. Gruer, Thin Solid Films, 509, (2004), 47.

[6] W. Nieveen, Appl. Surface Sci., 556, (2004), 231.

[7] M. Natasi, J.W. Mayer, J.K. Hirvonen, Ion-Solid Interactions: Fundamentals and Applications,

Cambridge University Press, New York, (1996).

[8] M. Mayer, SIMNRA User's Guide, Max-Plank-Institut Fur Plasmaphysik, Garching, Germany,

(2006).

[9] E. Szilagyi, F. Paszti, G. Amsel, Nuclear Instruments & Methods in Physics Research, Section B:

Beam Interactions with Materials and Atoms 100 (1995) 103.

[10] L.C. Feldman, J.W. Mayer, S.T. Picraux, Materials Analysis By Ion Channeling: Submicron

Crystallography, Academic Press, New York, (1982).

[11] Chan Taw Kuei, Ph.D. Thesis, National University Of Singapore, Singapore, (2009) and refs.

therein.

[12] KOBELCO, High Resolution RBS End Station System Documentation, Kobe, (2003).

[13] Mayer, J.W.; Tsaur, B. Y.; Lau, S. S. & Hung, L.S. Ion-beam-induced reactions in metal-

semiconductor and metal-metal thin film structures, Nucl. Instr. and Meth, 182/183, 1-13, (2001).

Bibliography

58

[14] Santos, D.L.; de Souza, J. P.; Amaral, L. & Boudinov, H. Ion beam mixing of Fe thin film and Si

substrate, Nucl. Instr. and Meth, 103, 56-59 (1995)

[15] Srivastava, S.K.; Avasthi, D. K.; Assaman, W.; Wang, Z. G.; Kucal, H.; Jacquet, E.; Carstanjen, H.

D. & Toulemonde, M.; Test of the hypothesis of transient molten state diffusion for swift-heavy-ion

induced mixing, Phys. Rev, 71, 0193405-0193408(2005).

[16] Diva, K.; Kabiraj, D.; Chakraborty, B. R.; Shivaprasad, S. M. & Avasthi, D. K. Investigation of V/Si

mixing induced by swift heavy ions, Nucl. Instr. And Meth, 222, 169-174 (2004)

[17] N. Manikanthababu, Chan Taw Kuei, A. P. Pathak, G. Devaraju, N. Srinivasa RaoYang Ping, M. B.

H. Breese, T. Osipowicz and S. V. S. Nageswara Rao , Ion beam studies of Hafnium based alternate

high-k dielectric films deposited on silicon, Nucl. Instr. And Meth in Phys. Res. B, (2014).

[18] D. K. Avasthi, G.K. Mehta , Swift Heavy Ions for Materials Engineering and Nanostructuring

Springer Series in Materials Science, 145, (2011) 1.

[19] Xiangkun Yu, Lin Shao, Q.Y. Chen, L. Trombetta, Chunyu Wang, Bhanu Dharmaiahgari, Xuemei

Wang, Hui Chen, K.B. Ma, Jiarui Liu, Wei-Kan Chu, Nucl. Instr. Meth. Phys. Res., B 249 (2006) 414.

[20] A. Benyagoub, Nucl. Instr. Meth. Phys. Res., B 245 (2006) 225.

[21] T. Osipowicz, H.L. Seng, T.K. Chan, B. Ho, The CIBA high resolution RBS facility, Nucl. Instr.

Meth. Phys. Res., B 249, 915-917 (2006)

[22] C.S. Ho, The Study of Ultra-thin Diffusion Barriers in Copper Interconnect System, Dissertation,

NUS, 2009.

Appendices

59

Appendices

Fig. A.1 Figure Splat profiles of a point spot of energy, E from 400 keV to 421 keV simulated through 2mm collimeter

Appendices

60

Fig. A.2 Splat profiles of a point spot of energy, E from 421 keV to 442 keV collimated by 1mm collimeter

Appendices

61

Fig. A.3 Height of the splat profiles for point and beam spots collimated by 2mm collimeter

Fig. A.4 Width of the splat profiles for point and beam spots collimated by 2mm collimeter

Appendices

62

Fig. A.5 Height of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)

Fig. A.6 Width of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)

Appendices

63

Fig. A.7 Centre position of the splat profile of the double focusing point at different starting x-position of the backscattered ion (1mm collimeter)

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