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
Introduction Chapter 1
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
Introduction Chapter 1
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
Physical Concepts Chapter 2
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.
Physical Concepts Chapter 2
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,
Physical Concepts Chapter 2
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)
Physical Concepts Chapter 2
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 ,
Physical Concepts Chapter 2
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,
Physical Concepts Chapter 2
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,
Physical Concepts Chapter 2
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.
Physical Concepts Chapter 2
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
Physical Concepts Chapter 2
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,
Physical Concepts Chapter 2
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
Physical Concepts Chapter 2
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
Physical Concepts Chapter 2
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.
Physical Concepts Chapter 2
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]
Physical Concepts Chapter 2
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
Physical Concepts Chapter 2
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
Physical Concepts Chapter 2
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
HRBS Set-up Chapter 3
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.
HRBS Set-up Chapter 3
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.
HRBS Set-up Chapter 3
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]
HRBS Set-up Chapter 3
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
HRBS Set-up Chapter 3
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.
HRBS Set-up Chapter 3
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]
HRBS Set-up Chapter 3
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
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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:
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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)
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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
Depth ( 1015 atoms/cm2)
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
Depth ( 1015 atoms/cm2)
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
Depth ( 1015 atoms/cm2)
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).
Study of Swift Heavy Ion Irradiation effects on Hafnium based high-k dielectric thin films deposited on Silicon
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.
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector 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:
Simulation and characterization of new 2-D focal plane detector using SIMion
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.
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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.
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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.
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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:
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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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
Simulation and characterization of new 2-D focal plane detector using SIMion
Chapter 5
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
Chapter 5
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
Simulation and characterization of new 2-D focal plane detector using SIMion
Chapter 5
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
Simulation and characterization of new 2-D focal plane detector using SIMion
Chapter 5
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)
Simulation and characterization of new 2-D focal plane detector using SIMion
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)
Simulation and characterization of new 2-D focal plane detector using SIMion
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
Simulation and characterization of new 2-D focal plane detector using SIMion
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
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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)