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Analysis of collision cascades in titanium deuteride by D-D fusion
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Workman, Thomas Wilson
(1992)
Analysis of collision cascades in titanium deuteride by D-D fusion.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/fa6m-mh68.
Abstract
As a test of the linear binary collision cascade model for ion-solid interaction, theoretical models of D-D fusion induced by heavy ion irradiation of titanium deuteride are compared with experimental results. Thin-film titanium deuteride samples of composition TiD
1.7
were prepared by heating 320 nm titanium films on silicon dioxide in a static pressure of deuterium. The deuterium content of these films was inferred from changes in the titanium and oxygen contaminant signals measured by 3.05 MeV oxygen-resonance backscattering spectrometry.
The titanium deuteride samples were irradiated with beams of argon and xenon ions with energies ranging from 140 to 600 keV. The energy of the incident ion was transferred to atoms in the sample through a series of nuclear collisions, resulting in deuteron-deuteron collisions with energies up to tens of keV. The cross sections for D-D fusion at these energies are large enough for fusion events to be detected for doses above 10
14
ions. A silicon surface-barrier detector placed at an angle of 130° with respect to the incident ion beam was used to monitor the 3.02 MeV protons and 1.01 MeV tritons from the D(d,p)T reaction and 0.82 MeV
He ions from the D(d,n)
He reaction. Fusion yields (fusion events per incident ion) ranging from 10
-14
to 10
-10
were measured.
A linear binary collision cascade model is presented which predicts fusion yields which are in excellent agreement with the measured yields for all cases studied. The model predicts a distribution of deuteron-deuteron center-of-mass velocities which causes a distribution of Doppler shifts in the spectrum of the fusion products. The shape of the theoretical proton signals based on the model is a reasonably good fit to the experimental proton signals.
The use of D-D fusion induced by heavy-ion irradiation for measuring deuterium concentrations is compared with currently used methods and is found to be somewhat less sensitive than nuclear reaction analysis, but suitable for measuring deuterium concentrations as low as 2 atomic percent with ion beams producible by ion implanters with an energy range of a few hundred kV.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Materials Science ; collision cascades ; titanium deuteride ; D-D fusion
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Materials Science
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Nicolet, Marc-Aurele
Thesis Committee:
Unknown, Unknown
Defense Date:
18 May 1992
Record Number:
CaltechETD:etd-08172007-080314
Persistent URL:
DOI:
10.7907/fa6m-mh68
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3158
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ANALYSIS OF COLLISION CASCADES IN TITANIUM
DEUTERIDE BY D—-D FUSION
Thesis by
Thomas Wilson Workman
In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
California Institute of Technology
Pasadena, California
1992
(Defended May 18, 1992)
~ii—
To Kimi
~ ii -
ACKNOWLEDGEMENT
First and foremost, I wish to thank Professor Marc-A. Nicolet. His support,
inspiration, and guidance have made my undergraduate and graduate study at
Caltech a very rewarding experience.
Dr. W. L. Johnson was instrumental in the conceptualization of the experi-
ments leading up to this thesis. Dr. C. A. Barnes gave valuable guidance in the
matters of nuclear physics and contributed ideas as to additional areas of exploration
with D—D fusion.
I would like to thank the members of Professor Nicolet’s group, past and
present, especially Drs. Y-T. Cheng, and T. Banwell, who taught me the basics
of ion-solid interactions; also Dr. E. Kolawa, Dr. G. Bai, and J.S. Chen, who have
contributed, through either collaborations or casual conversations, to the comple-
tion of this thesis. Particular acknowledgments are due to Dr. H. Fecht, who
helped with the early work in creating titanium hydride thin films and to Chang
Liu, who lead me through the process of fabricating Si3N, filters. For their techni-
cal assistance, I am indebted to B. Stevens, M. Easterbrook, D. Groseth, and most
especially, R. Gorris, who built, modified, or cajoled into working every piece of
equipment I have utilized in the performance of this work.
I am grateful for the encouragement and support of my parents, who pointed
me in the right direction and then let me make my own decisions.
Finally, I wish to express my utmost appreciation to my wife, Kimi, for her un-
conditional love and support during my long study, her indulgence of my scientist’s
ways, and her great help in the preparation of this manuscript.
—iv-
ABSTRACT
As a test of the linear binary collision cascade model for ion-solid interac-
tion, theoretical models of D—D fusion induced by heavy ion irradiation of titanium
deuteride are compared with experimental results. Thin-film titanium deuteride
samples of composition TiD,,7 were prepared by heating 320 nm titanium films on
silicon dioxide in a static pressure of deuterium. The deuterium content of these
films was inferred from changes in the titanium and oxygen contaminant signals
measured by 3.05 MeV oxygen-resonance backscattering spectrometry.
The titanium deuteride samples were irradiated with beams of argon and xenon
ions with energies ranging from 140 to 600 keV. The energy of the incident ion was
transferred to atoms in the sample through a series of nuclear collisions, resulting in
deuteron—deuteron collisions with energies up to tens of keV. The cross sections for
D-—D fusion at these energies are large enough for fusion events to be detected for
doses above 104 ions. A silicon surface-barrier detector placed at an angle of 130°
with respect to the incident ion beam was used to monitor the 3.02 MeV protons
and 1.01 MeV tritons from the D(d,p)T reaction and 0.82 MeV *He ions from the
D(d,n)*He reaction. Fusion yields (fusion events per incident ion) ranging from
10-14 to 107! were measured.
A linear binary collision cascade model is presented which predicts fusion yields
which are in excellent agreement with the measured yields for all cases studied. The
model predicts a distribution of deuteron—deuteron center-of-mass velocities which
causes a distribution of Doppler shifts in the spectrum of the fusion products. The
shape of the theoretical proton signals based on the model is a reasonably good fit
to the experimental proton signals.
The use of D-D fusion induced by heavy-ion irradiation for measuring deu-
terium concentrations is compared with currently used methods and is found to be
somewhat less sensitive than nuclear reaction analysis, but suitable for measuring
deuterium concentrations as low as 2 atomic percent with ion beams producible by
ion implanters with an energy range of a few hundred kV.
~vi-
TABLE OF CONTENTS
Acknowledgement
Abstract
Table of Contents
List of Figures
List of Publications
’ Chapter 1 Introduction
1.1 Origin of Experiment
1.2 The Collision Cascade
1.3 The D-D Reaction
Chapter 2 Sample Preparation and Characterization
2.1 Fabrication of TiD Thin Films
2.2 Backscattering Analysis of TiD Thin Films
2.2.1 Oxygen Resonance for Determination of Oxygen
Concentration
2.2.2 Determination of Deuterium Concentration
2.3 X-ray Diffraction Analysis
Chapter 3. Experimental Procedures and Results
3.1 Experimental Setup
3.2. Experimental Procedures
3.3. Experimental Results
3.3.1 Al Filter Results
3.3.2 SizN, Results
ili
iv
vi
Vill
XiV
19
19
27
27
34
38
42
42
48
52
o2
ov
-~ vu -
Chapter 4 Binary Collision Cascade Model of Fusion Yield
4.1 Introduction
4.2 Representation of the Collision Cascade
4.3 Calculation of the Fusion Yield of a Chain
4.4 Algorithms Used to Compute Fusion Yields
4.5 Results and Comparison with Experiment
4.5.1 Model Results for Xe Irradiation
4.5.2 Model Results for Ar Irradiation
4.5.3 Comparison of Model with Experiment
Chapter 5 Doppler Analysis of Peak Shapes
5.1 Processes Affecting Peak Shape
5.2 Modeling the Deuteron Energy Spectrum
5.3 Model Results
5.4 Calculation of the Doppler Shift
5.5 Comparison with Experiment
64
64
65
67
70
72
73
16
78
83
84
85
89
94
98
Chapter 6 Considerations on Applications to Materials Analysis 102
6.1 Comparison with Existing Techniques
6.2 Optimum Parameters for Measuring Deuterium
Concentration
Appendix 1 Fabrication of Thin Si3N, Filters
Appendix 2 FORTRAN Program Used to Calculate Fusion Yields
102
104
111
114
Fig. 1.1
Fig. 1.2
Fig. 2.1
Fig. 2.2
Fig. 2.3a
Fig. 2.3b
— Vili —
LIST OF FIGURES
The interatomic potential for D—D interaction. For r < R the deep neg-
ative potential is due to the strong nuclear force. For r > R the coulomb
and centrifugal potentials present a barrier which must be penetrated
for a reaction to occur (taken from [24]). 12
Experimental S(£)-factor data for the reactions (a) D(d,p)T and
(b) D(d,n)*He. The solid curves are the results of polynomial fits to
the data for Ecyy <120 keV (taken from [25]). 14
Angular distributions at representative energies for D(d,p)T and
D(d,n)*He reactions. The solid curves through the data points are
the results of x? analysis using even Legendre polynomials (taken from
[25]). 15
Pressure-composition isotherms for the Ti-H system. 21
Schematic of furnace system used for hydiding and deuteriding Ti
samples. 22
3.08 MeV He** backscattering spectra of sample Til0 before and af-
ter deuteridation, with the 3.05 MeV oxygen resonance occurring at a
depth of 80 nm. 32
Background subtracted oxygen signals (data points) and Gaussian fits
to oxygen resonance signals (lines) for the spectra shown in Fig. 2.3a.
32
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 2.7
Fig. 2.8a
Fig. 2.8b
Fig. 3.1
Fig. 3.2
Fig. 3.3a
—ix-
Oxygen concentration as a function of (assumed) deuterium concentra-
tion for sample Til0 based on the peak height of the oxygen resonance
signal and Eq. 2.6. The two dashed lines delineate the range of uncer-
tainty in y. 33
2 MeV RBS spectrum of sample Til0 (tilted 20°) before and after
deuteridation. Ti signal height decreases and width increases due to
the energy absorption of deuterium. 36
Intersection of Eq. 2.6 and Eq. 2.10 which determines oxygen and deu-
terium concentrations for sample Ti10. The intersection point indicates
a composition of Tig.36Do.6300.01. The dashed lines delineate the range
of uncertainty for each equation. 37
Ti-H phase diagram. The hydrogen concentration as determined by
backscattering analysis (6142 at%) is near the border between the
fec 6 phase and the fct ¢ phase. 39
X-ray spectrum of pure Ti sample before hydridation. 40
X-ray spectrum of Ti sample after hydridation to TiH;.7. The peaks are
consistent with an fcc structure with a lattice parameter of 4.530 A.
40
Schematic of 400MPR Ion Implanter used for ion irradiation. 43
Top and side views of detector~sample geometry. 45
Background spectrum taken with no beam and no TiD;.7 sample over
a duration of 14 hours. Background count rate = 18 counts/hour. 51
Fig. 3.3b
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 3.8
Fig. 4.1la
_— x _
Background spectrum taken during 250 keV Xe?™ irradiation of TiHj.7.
Total ion dose = 6.0x10!® ions over a duration of 75 minutes. Back-
ground count rate = 15 counts/hour. 51
Spectrum obtained by irradiating TiD;.7 with 5.12 10!® 400 keV Artt
ions over a duration of 5.5 hours. A 5 ym Al filter was placed in
front of the detector to block sputtered and backscattered particles.
The detector was placed at an angle of 129° from the incident beam
direction and subtended a solid angle of 44.1 mSr. 53
Record of ion dose and proton and triton counts taken during 400 keV
Art? irradiation of TiD, 7. 55
Spectrum obtained by irradiating TiD,.7 with 1.53x10?* 500 keV Xett
ions over a duration of 3 hours. A 540 nm Si3N, filter was placed in
front of the detector to block sputtered and backscattered particles.
The filter was thin enough to allow the 0.82 MeV *He to reach the
detector. The detector was placed at an angle of 130° from the incident
beam direction and subtended a solid angle of 50.8 mSr. 58
Record of ion dose and proton, triton, and *He counts taken during
500 keV Xet+ irradiation of TiD, 7. 59
Experimental fusion yields for Ar and Xe irradiation of TiD,.7 using
an Al filter (©) or a SisN, filter (A) in front of the detector. 62
Theoretical fusion yields for the first three generations of recoils for
Xe irradiation of TiD,.7. The dotted line is the highest yield for 4%
generation recoils (Yxerititipp )- 74
Fig. 4.1b
Fig. 4.2a
Fig. 4.2b
Fig. 4.3a
Fig. 4.3b
Fig. 4.4
Fig. 5.1
The relative contributions (>10~°) to the total fusion yield for the
chains shown in Fig 4.1a. 74
Theoretical fusion yields for the first three generations of recoils for
Ar irradiation of TiD,.7. The dotted line is the highest yield for 4%
generation recoils (YartititTipp )- (7
The relative contributions (>107°) to the total fusion yield for the
chains shown in Fig 4.2a. 77
Comparison of theoretical fusion yields for six different interatomic
potentials (lines) and experimental fusion yields (data points) for Ar
irradiation of TiD, 7. 79
Comparison of theoretical fusion yields for six different interatomic
potentials (lines) and experimental fusion yields (data points) for Xe
irradiation of TiD,.7. 79
Comparison of theoretical (lines) and experimental (data points) fusion
yields for Ar and Xe irradiation of TiD;.7._ Theoretical yields were
calculated using the Thomas-Fermi-Sommerfeld interatomic potential,
which gives the best fit to the experimental data. 80
Comparison of theoretical and experimental fusion spectra for
500 keV Xett irradiation of TiD,.7. Theoretical yields assume mono-
energetic beams of 3.02 MeV protons, 1.01 MeV tritons, and 0.82 MeV
*He ions emitted from the sample surface convoluted with the detected
energy loss distribution of Table 5.1. The area under each theoretical
signal is equal to the area under the corresponding experimental signal.
86
Fig. 5.2a
Fig. 5.2b
Fig. 5.3
Fig. 5.4a
Fig. 5.4b
Fig. 5.5a
Fig. 5.5b
Fig. 6.1
— xii —
Theoretical deuteron energy distributions for 600 keV Artt irradiation
for the three chains giving the largest contribution to the total fusion
yield. 91 .
Theoretical deuteron energy distributions for 200 keV Xe? irradiation
for the three chains giving the largest contribution to the total fusion
yield. The maximum deuteron energy for the Xe—D chain is 11.9 keV.
91
Theoretical fusion yield as a function of deuteron energy at the time of
fusion for Ar irradiation at the energies used in the experiment. Each
peak is dominated by the Ar—-D--D chain contribution to greater than
99.2%. 92
Theoretical fusion yield as a function of deuteron energy at the time of
fusion for Xe irradiation at the energies used in the experiment. The
high energy tails are due to the Xe-Ti-D-D chain contribution. 93
Enlarged view of the fusion yield for 200 keV Xe irradiation explicitly
showing the contributions of the Xe-D-D and Xe-Ti-D-D chains. 93
Comparison of unidirectional (@ = 130°) and distributed angle (with
33% Nuclear Stopping) models and the experimental proton signal for
600 keV Art* irradiation. 99
Comparison of unidirectional (@ = 130°) and distributed angle (with
40% Nuclear Stopping) models and the experimental proton signal for
200 keV Xe? irradiation. 99
Comparison of theoretical fusion yields for irradiation of TiD,.7 with
various ions. 105
— xiii -
Fig. 6.2 Theoretical fusion yields as a function of deuterium concentration for
1 MeV and 500 keV Ar and Ne ions. The detection limit for 500 keV
ions is 4 at%, and for 1 MeV, it is 3 at% for Ne and 2 at% for Ar.
108
Fig. A1.1 Procedure for fabricating thin Si3N, filters. 113
— xiv —
LIST OF PUBLICATIONS
“D(d,p)T Fusion Induced by Heavy Ion Irradiation of TiD, 7,” T. W. Workman
and M-A. Nicolet, submitted to Phys. Rev. Lett. 1991.
“Ion Mixing of Metal/Al Bilayers near 77 K,” E. Ma, T. W. Workman, W. L.
Johnson, and M-A. Nicolet, Appl. Phys. Lett. 54, 413 (1989).
“Interfacial Reactions of Mo with Al: Ion Mixing Versus Thermal Annealing”
E. Ma, A. J. Brunner, T. W. Workman, C. W. Nieh, X.-A. Zhao, and M-A.
Nicolet, Mat. Res. Soc. Symp. Proc. 100, 75 (1988).
“Ion Beam Mixing of Amorphous Cr-Nitride / Mo-Nitride and Polycrystalline
Cr/Mo Bilayers,” M. Thuillard, T. W. Workman, E. Kolawa, and M-A. Nicolet,
Journal of Less-Common Metals 145, 505 (1988).
“Studies of a Phenomenological Model of Ion Mixing” Y.-T. Cheng, T. W.
Workman, M-A. Nicolet, and W. L. Johnson, Mat. Res. Soc. Symp. Proc. 74,
419 (1987).
“Effect of Thermodynamics on Ion Mixing,” T. W. Workman, Y.-T. Cheng,
W. L. Johnson, and M-A. Nicolet, Appl. Phys. Lett. 50, 1485 (1987).
“Correlation Between the Cohesive Energy and the Onset of Radiation-
Enhanced Diffusion in Ion Mixing,” Y.-T. Cheng, X.-A. Zhao, T. Banwell,
T. W. Workman, M-A. Nicolet, and W. L. Johnson, J. Appl. Phys. 60, 2615
(1986).
“Ion Beam Modification of Corrosion and Wear Properties of Metals and Ce-
ramics,” T. W. Workman (sponsored by ITT, presented Fall 1985).
—-l1-
Chapter 1
INTRODUCTION
1.1 Origin of Experiment
This body of work was born out of a study of ion mixing in metallic bilayers [1].
We had found that the mixing efficiency under ion irradiation by heavy ions (i.e.,
Ar and Xe) scaled with the (negative) heat of mixing of the bilayer (AH iz) [2].
That is, the more exothermic the reaction between the two layers, the larger the
spreading of the interface for a given ion dose. Thus, a chemical driving force
with an energy on the order of 1 eV/atom profoundly affects the mixing caused
by ions with an incident energy of several hundred keV. This result ran counter
to the prevailing theory that ion mixing was a purely ballistic process depending
only upon the masses of the atoms in the bilayer [3]. However, the results were
consistent with those expected for “thermal spike” mixing.
The “thermal spike” model describes the evolution of the collision cascade pro-
duced in a solid by heavy ion irradiation from a linear binary collision cascade at
high energies (keV and above) to a “space filling” cascade involving a majority of
atoms in a localized region at low energies (~10 eV) [4]. The energies of atoms
within this region are assumed to reach a roughly Boltzmann distribution equiva-
lent to a temperature on the order of 10* K for a duration of approximately 1 ps [5]
(thus, the name “thermal spike”). During this time, atoms within the region un-
dergo random walk diffusion. When the thermal spike coincides with the interface,
the diffusion will be biased by the gradient in chemical potential due to the heat
of mixing of the bilayer. From our experimental results [1,2,6,7], it appears that
mixing within the thermal spike is the dominant mechanism of mixing for heavy
~ 2 -
ion irradiation in bilayers of average atomic number > 20.
The titanium/platinum system has one of the largest negative heats of mixing
(AH mic = —122 kJ/gr-atom [8]) of the systems we have studied, and, as expected,
it has one of the highest mixing efficiencies. However, we found that the heat of
mixing of the system could be changed from highly negative to positive by adding
hydrogen to the Ti layer. This change comes about because hydrogen is insoluble in
Pt, and TiH, has a lower free energy than any TiPt compound [9]. Because of this
drastic change in AH,,;, and the fact that the addition of hydrogen would have very
little effect on the “ballistic properties” of the bilayer under heavy ion irradiation
(due to hydrogen’s low mass), we felt that a comparison of the ion mixing of Ti/Pt
and TiH,/Pt bilayers would be quite enlightening.
At the time that we were conceiving this experiment, Fleischmann and Pons
announced the discovery of “cold fusion” [10]. In the rush of experiments that
followed, “cold fusion” was reported to be detected in palladium deuteride and ti-
tanium deuteride samples under various conditions, such as in electrolytic cells [11]
and in heating and cooling between room temperature and liquid nitrogen temper-
ature [12]. It was theorized that putting these materials in non-equilibrium states
could possibly lead to a huge increase in the D-D fusion rate [13].
Realizing that the conditions existing in the thermal spike regime of a collision
cascade were extremely far from equilibrium, we saw a chance to do two exper-
iments in one by changing the TiH2/Pt samples to TiD2, and looking for fusion
products during ion mixing. After further thought on the collision cascade process,
we determined that head-on collisions between incident ions (with energies of sev-
eral hundred keV) and deuterons could transfer enough energy to a deuteron to
give it a significant chance of colliding with another deuteron and fusing. This type
of fusion event could be explained by the “normal” D-D fusion cross section, and
~ 3 -
therefore, would not require the existence of “cold fusion.” Thus, any fusion events
occurring could be due to either high energy deuterium recoils in the early stages
of the collision cascade, or “cold fusion” in the later, thermal spike region of the
cascade. If fusion events from the high energy deuterium recoils dominated, the
fusion products could be used as a probe (similar to nuclear reaction analysis) of
either the deuterium content of the sample or the collision cascade process itself. If
the “cold fusion” contribution dominated, we could learn more about the thermal
spike process. Even if no fusion events were detected, we would still have the ion
mixing results. Therefore, the experiment had great potential.
Having decided on the aims of the experiment, the next step was to fabricate the
TiD2/Pt samples. This turned out to be much more difficult than first anticipated.
An existing hydrogen furnace was used to deuteride thin films of Ti. The titanium
deuteride films produced invariably had a thick (~30 nm) surface layer of TiO.
This was unacceptable for the experiment because the Pt layer had to be deposited
after the deuteridation process to avoid interdiffusion between the layers during
deuteridation. Therefore, the TiD2/Pt interface would be contaminated by the
thick oxide layer, which would severely affect the ion mixing. (It would essentially
be a study of the ion mixing of TiO2/Pt instead of TiD2/Pt.) Many attempts were
made to improve the furnace to reduce the oxygen contamination and to backsputter
off the oxide layer from the sample, but all were unsuccessful. Therefore, the Pt
layer was put aside, and the aim of the experiment was changed to include just the
search for fusion events due to the ion irradiation of titanium deuteride.
Later, a whole new hydridation furnace was built (see Section 2.1) that could
produce titanium deuteride samples suitable for the TiD2/Pt experiment. By that
time, financial support for the project had been discontinued and that experiment
was dropped.
1.2 The Collision Cascade
The chain of events that occur as an energetic ion penetrates a solid are of |
great interest to those studying ion implantation, ion mixing, and ion analysis
techniques [14,15]. Direct observation of the collision cascade within the solid is
difficult due to the extremely short time scale (~107!! sec) and small distances
(< 1 ym) involved. Direct observations of the collision cascade have so far been
limited to sputtered particles [16]. The majority of information about the collision
cascade has come from indirect observations.
Experimental data giving indirect information about the collision cascade in-
clude ion range and range straggling, concentration of defects produced by ion
irradiation, and the spreading of an interface between two different atomic species
(ion mixing). Each of these quantities is measured after ion irradiation. Electronic
processes, such as Auger electron emission and x-ray emission, caused by the col-
lision cascade can also be analyzed to give information about the cascade itself.
For example, Auger electron emission from sputtered atoms or atoms in the near
surface region (the first 3 nm) can be used to analyze the near surface portion of the
cascade [17,18]. X-ray production during ion irradiation of thick targets has been
compared to calculated x-ray cross sections using a simple model of the collision
cascade [19]. However, analyzing the cascade by use of signals of electronic nature
has two drawbacks. The first is that the processes that create these particles are
indirect in relation to the nuclear collisions involved in the cascade. The second
(which is especially important for Auger processes) is that the detected particles
(electrons and x-rays) undergo capture or attenuation over the course from the point
where they are created to the surface, where they are detected. As the depths at
which these particles are created is unknown, correction of the attenuation factor
is not straightforward.
~5-
Another measurement that gives information about the collision cascade is nu-
clear reaction analysis. Normally, nuclear reaction analysis involves irradiating a
target with a high energy ion that undergoes a nuclear reaction with an atom in
the target, creating a different particle with an energy characteristic of the reac-
tion. Thus detecting the reaction product gives information about nuclear collisions
between the primary ion and the target atoms. In the present investigation, the
incident ion does not undergo a nuclear reaction with an atom in the target, but
transfers energy to an atom in the target (possibly through any number of interme-
diate collisions) which then undergoes a nuclear reaction with another target atom.
In this case, information can be obtained about primary and higher generation recoil
atoms in the collision cascade. The particles detected (3.02 MeV protons) are pro-
duced directly from the nuclear collisions of the cascade and have sufficient energy
to reach the surface from the depth at which they were created and be detected.
Even with the lack of direct observation of the collision cascade within a solid,
enough indirect information has been collected to adjust theoretical descriptions of
the cascade processes to match closely most observable effects of ion irradiation of
solids. The important parameters which must be specified to account for exper-
imental observations include the energy loss of the ion and energetic recoils, the
cross sections for ion—atom and atom-atom collisions, and the number and types of
defects produced during the cascade. The production of defects is not important
to this study, and will not be discussed further. Knowledge of the scattering cross
sections is necessary to determine the energy distribution of primary and higher
generation recoils in the cascade. Knowledge of the mechanisms of energy loss are
necessary to determine the fraction of the ion energy going towards nuclear displace-
ments. In metals and semiconductors, ion—-electron collisions do not contribute to
atomic displacements; therefore, in terms of the chain of nuclear displacements, the
—~6-
energy loss from ion-electron collisions simply acts to attenuate the incident ion
energy between nuclear collisions.
To calculate the differential scattering cross section do/dT for ion—atom and .
atom-atom collisions (where T is the energy transferred to the target atom), the
appropriate interatomic potential for the atomic masses and range of interaction
energies must be known. The method of calculating the differential scattering cross
section for a given interatomic potential is explained in detail in [20]. For ion
energies in the keV range and above, the appropriate potential lies between the hard
sphere and coulomb potentials. For the hard sphere potential, do /dT is a constant,
i.e., all energy transfers are equally likely. For the coulomb potential, da/dT varies
as 1/T”, i.e., low energy transfers dominate. In the limit of high incident ion energy
(MeV range), the coulomb potential best fits experimental results. However, as the
interaction energy decreases, the effect of electron screening of the nuclear charges
becomes significant, and a correction becomes necessary.
The general method of correcting for electron screening is to multiply the
coulomb potential by a screening function ¢(r/a)
V(r) = Aatne’ (“) (1.1)
r a
where Z; and Z2 are the atomic numbers of the incident ion and target atom,
respectively, e is the electronic charge (3.79 x 1077 (MeV cm)}/?), and a is called
the screening length, a commonly used value of which is the Firsov screening length,
which is given by
0.885349
(2,3? + Z1!?)2/8
an
; (1.2)
where dp is the first Bohr radius (0.52917 A). The forms of the six screening func-
tions considered in this work are listed in Table 1.1. It is not possible to calculate
the differential cross section for these potentials in terms of analytical functions;
-7-
therefore, fits to the differential scattering cross section involving analytic functions
and three adjustable parameters have been calculated [21]. Each of these screening
functions has been adjusted to agree with experimental observations for varying
ranges of incident ion energy and ion and target masses. The differential scatter-
ing cross sections for any of these six interatomic potentials should be expected to
accurately describe the ion—atom and atom-atom collisions for the relatively high
energies involved in this work.
Table 1.1 The electron screening functions for the six screened coulomb potentials
considered in this work [21].
Potential Form Constants
Thomas-Fermi-Sommerfeld ¢(r) = (1 + (23/144) 1/4) A = 0.2678
Bohr b(t) =e"** A=1
Lenz-Jensen d(x) = qQ,x)e7rV* d = (875/253)1/?
Lindhard [c?=1.8] o(x) =1—2/V2? +c? ce =1.8
Lindhard [c?=3.0] c? = 3.0
Moliére o(x) = 0.35e7** + 0.55e- 447 +
0.167204 A = 0.8
The energy loss of the incident ion and energetic recoils is the sum of the nuclear
and electronic energy losses. The nuclear energy loss is the result of the discrete
collisions described above. The electronic energy loss is normally approximated as
a continuous process, as opposed to a series of discrete ion-electron collisions. For
relatively low energy ions (~10 keV/amu) in metals, the electronic energy loss is
reasonably well approximated by the Lindhard—Scharff formula [22], in which the
energy loss is proportional to the ion velocity v
(=) =k, k= Z,1/8 ore Neo 7172 (1.3)
dz) rs v9 (Zy 4 gl 3/2
—~g8-
where Z, and Z_ are the atomic numbers of the incident ion and target atom,
respectively, N is the atomic density of the target, and vo is the Bohr velocity
(Z,e"/h). At higher energies, the electronic energy loss increases less rapidly with
energy, reaches a peak value, and then decreases with increasing energy. The
peak in electronic energy loss occurs at ion velocities slightly higher than the
“Thomas—Fermi” velocity Z,~?/*v9, which correspond to an energy of approxi-
mately (25 keV/amu) Z,*/ M, (50 keV for D, 47 MeV for Ar). At velocities greater
than the “Thomas—Fermi” velocity, the electronic energy loss is well described by
the Bethe-Bloch formula [23]
(=) _ 8 Z,7e4 In(eg +14 5/ez) _ 4m.E
BB
dE — 2M 1.4
dz T eB > BS TERI’ (1.4)
where m, is the electron mass and the energy IJ is an average of the various ex-
citations and ionizations of the electrons in a target atom and is of the order of
approximately 10 eV. The transition in electronic energy loss between Lindhard-
Scharff and Bethe-Bloch regimes is well described by the harmonic mean [23]:
dE 1 1 ~
dB\ | 1.5
(=). ( dE) Ey) ;
In compound targets (i.e., targets containing more than one element), the en-
ergy loss is the sum of the losses in the constituent elements, weighted according to
their atomic concentration in the compound. This is known as Bragg’s rule.
The irradiating ions in this work are Ar and Xe with energies up to 600 keV.
The maximum energy transferrable T,,., to the target atoms (Ti and D) by an ion
with energy FE is given by
where M, and Mp, are the ion and target atomic masses, respectively. Thus, the
maximum fraction of ion energy transferred directly from the ion to a deuteron is
—~Q-
18.3% for Ar and 5.95% for Xe. For ion—Ti energy transfers, the maximum fractions
are 99.2% (Ar) and 78.3% (Xe). Therefore, the maximum possible deuteron energy
is 110 keV (for 600 keV Ar irradiation). This energy is high enough to require
use of the Bethe-Bloch formula for determination of the electronic energy loss for
the highest energy deuterons. The electronic energy loss of all other particles is
adequately described by the Lindhard—Scharff formula.
The information above on differential scattering cross sections, electronic en-
ergy loss, and maximum energy transfer is sufficient to accurately describe the
collision cascade caused by Ar and Xe irradiation of titanium deuteride. This in-
formation will be used in Chapter 4 to calculate the theoretically expected fusion
yields for ion irradiation of titanium deuteride.
1.3 The D—-D Fusion Reaction
Following the treatment of Clayton [24], a nuclear reaction occurs when a
particle a strikes a nucleus X producing a nucleus Y and a new particle 6 is
symbolized by
a+X—->Y+6, or X(a,b)Y.
In the course of this reaction, the total energy (kinetic energy plus rest-mass energy),
momentum, and angular momentum are conserved. The conservation of mass and
energy requires that for the reaction X(a,b)Y
Bax + (Ma + Mx)ec’ = py + (At, + My )c? ; (1.7)
where FE, x is the sum of the kinetic energies of a and X in the center-of-mass frame,
Ey is a similarly quantity for b and Y, M, is the rest mass of a, etc. The energy
liberated by a reaction in which the mass of the products is less than that of the
—~10—
reactants will be shared by the reaction products such that the total momentum in
the center-of-mass frame remains zero:
Mi Esy E My Exy
_ | B= ae 18
M, + My > My + My (1.8)
The D-D nuclear reactions of interest in this work are D(d,p)T and D(d,n)?He.
The atomic numbers (Z), numbers of nucleons (A), and atomic masses of the rele-
vant particles are listed in Table 1.2. The energy liberated in the D(d,p)T reaction
is 4.03 MeV, and that liberated in the D(d,n)*He is 3.27 MeV. These energies are
divided among the reaction products such that in the center-of-mass frame
D+D-— T(1.01 MeV) + p(3.02 MeV)
D+D — *He(0.82 MeV) + n(2.45 MeV).
A third reaction,
D+D-— ‘*He + 7(23.85 MeV),
is also possible, but has a cross section which is seven orders of magnitude smaller
than the two reactions above and will not be mentioned further.
Table 1.2 Atomic masses and energy equivalents of reactants and products of D-D
nuclear reactions (Information taken from Ref 24).
Element Z A Mass Energy Equivalent
(amu) (MeV)
n 0 1 = 1.00867 939.549
H 1 1 1.00783 938.767
D 1 2 2.01410 1876.092
T 1 3 3.01605 2809.384
3He 2 3 3.01603 2809.365
*He 2 4 4.00260 3728.337
-1l1l-
In order for two particles to undergo a nuclear reaction, the two nuclei must
be brought close enough together to be within the range of the strong nuclear
force, i.e., the center-to-center separation must be less than the range of the nuclear
force (~107'° m) plus the sum of the nuclear radii. This distance, known as the
interaction radius R, is generally given as [24]
R=14(Ai" + A) fm, 1fim=10-% m, (1.9)
where A; and A» are the number of nucleons of the interacting particles. For
D-D reactions, the interaction radius is approximately 3.5 fm. To achieve such a
small separation, the particles must penetrate the coulomb barrier and (for non-zero
quantized angular momentum) the centrifugal barrier.
The probability of finding the particles with a separation less than R, can
be found by solving the radial component of the time-independent Schrédinger
equation
_h &x(r)
aa ae? + V(r) ~ Elx(r) =0, (1.10)
where x(r)=ry(r), w is the reduced mass of the interacting particles, and V(r) is
defined by:
r 2pr2
Z1 Zoe Ul+1)h? where the first term is the coulomb potential, the second is the centrifugal poten- for the case of D—D reactions, the effects of the centrifugal barrier are comparable ~12- _ ul+ 1h? oz 20" J r 2ur Figure 1.1 The interatomic potential for D-D interaction. For r < R the deep ~13- to those of the coulomb barrier. The centrifugal barrier will inhibit increasingly In the present work, the energy FE of the deuterons is significantly less than the form o(E) = ”) exp (eo = ) exp (-a7) (1.11) where E is the energy of the interacting particles in the center-of-mass frame, v The D(d,p)T and D(d,n)*He reactions were investigated for center-of-mass en- for energies less than approximately 30 keV. ~14- 120 ae | | een ns eee nee es ees eee ee eee ee ee ee cee eee 0 0 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Figure 1.2 Experimental S(E£)-factor data for the reactions (a) D(d,p)T and ~15— Did.p) T D (dn) “He Figure 1.3 Angular distributions at representative energies for D(d,p)T and —~16- Another study measured fusion cross sections for center-of-mass energies of In this thesis, D-D fusion within titanium deuteride was studied. The mean experiment. -~17- References (1] T. W. Workman, Y. T. Cheng, W. L. Johnson, and M-A. Nicolet, Appl. Phys. [2] Y. T. Cheng, M. Van Rossum, M-A. Nicolet, and W. L. Johnson, Appl. Phys. [3] P. Sigmund and A. Gras-Marti, Nucl. Instrum. Methods 182/183, 25 (1981). [4] Y. T. Cheng, M-A. Nicolet, and W. L. Johnson, Phys. Rev. Lett. 58, 2083 [5] T. Diaz de la Rubia, R. S. Averback, R. Benedek, and H. Hsieh, J. Mater. Res. [6] M. Van Rossum, Y. T. Cheng, M-A. Nicolet, and W. L. Johnson, Appl. Phys. [7] E. Ma, T. W. Workman, W. L. Johnson, and M-A. Nicolet, Appl. Phys. Lett. [8] A. R. Miedema, Philips Tech. Rev. 36, No. 8, 217 (1976). [11] S. E. Jones, E. P. Palmer, J. B. Czirr, D. L. Decker, G. L. Jensen, J. M. Thorn, [12] A. De Ninno, A. Frattolillo, G. Lollobattista, L. Martinis, M. Martone, L. Mori, [13] S. E. Koonin,“Enhancement of cold fusion rates by fluctuations,” April 17, —~18- [14] P. D. Townsend, J. C. Kelly, and N. E. W. Hartley, Jon Implantation, Sputtering [15] R. S. Averback, Nucl. Instrum. Methods B 15, 675 (1986). [16] R. Behrisch (ed.), Sputtering by Particle Bombardment I, Topics Appl. Phys. 17] T. D. Andreadis and J. Fine, Nucl. Instrum. Meth. 209, 495 (1983). 18] O. Grizzi and R. A. Baragiola, Phys. Rev. A 35 135 (1987). 19] K. Taulbjerg and P. Sigmund, Phys. Rev. A 5, 1285 (1972). [20] S. Geltman, Topics in Atomic Collision Theory (Academic, New York, 1969). [21] K. B. Winterbon, Rad. Effects 13, 215 (1972). [22] J. Lindhard and M. Scharff, Phys. Rev. 124, 128 (1961). [23] J. P. Biersack, E. Ernst, A. Monge, and S. Roth, Tables of Electronic and [24] D. D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (McGraw- [25] A. Krauss, H. W. Becker, H. P. Trautvetter, and C. Rolfs, Nucl. Phys. A 465, [26] J. Roth, R. Behrisch, W. Moller, and W. Ottenberger, Nucl. Fusion 30, 441 (1990). ~19— SAMPLE PREPARATION AND CHARACTERIZATION 2.1 Fabrication of Titanium Deuteride (TiD) Thin Films The desired sample composition and configuration was determined by the re- Thin films of Ti were prepared by electron-beam evaporation in an oil-free 500 nm thermally-grown SiOz surface layer. After the Ti evaporation, the wafer ~ 20 — was cut into 1.2 cm squares for the deuteridation process. Backscattering analysis bulk and a surface layer of TiO2 approximately 3 nm thick. To produce titanium deuteride, titanium was heated in a deuterium ambient at Considering the need for a pressure of a few atmospheres, the relatively high TiH films were produced, only then was the system switched to deuterium. The system used for deuteriding the samples is composed of a quartz tube 28 inches long, and is sealed to a 2.75 inch Conflat-type flange. This is connected ~21- ATOMIC PERCENT H 7 (0 20 30 40 50 60 70 atmospheric pressure aA 0 02 04 06 08 10. 12 14 16 18 30 23 Figure 2.1 Pressure-composition isotherms for the Ti-H system. 24 —~ 99 — : I} KO T.C. [1 Pressure Pressure Furnace Magnet Valve Mechanical Figure 2.2 Schematic of furnace system used for hydiding and deuteriding Ti ~ 23 - to a 4-way cross. Samples are loaded from the opposite side of the cross, which pressure indefinitely without a noticeable loss of pressure. A quartz boat (with a capacity of four 1.2 cm square samples) is used to hold and deuterium gases used was 99.95%. The procedure for hydriding the samples was as follows: A quartz basket con- loaded into the quartz boat, and the boat assembly was loaded into the system and — 24 — positioned so that the samples remained outside of the furnace. The system was fixed at this level. The furnace was turned on and set at 700°C. A temperature of 700°C was contamination was minimized. The parameters modified between different runs were hydriding pressure, tem- ture. Also, the Ti getter absorbed hydrogen as well as oxygen, with the amount of ~ 25 ~ hydrogen absorbed dependent on the amount of getter used. Therefore, no effort hydrogen content of the titanium hydride films produced. Hydrides could not be produced at temperatures below 400°C due to the pres- removing the barrier to the absorption of hydrogen. Titanium samples annealed at 350°C for 20 hours at a hydrogen pressure of into the bulk at higher temperatures. Experiments at temperatures above 400°C (i.e., 425, 450, and 500°C) with fixed trations with increasing temperature, just as predicted by the pressure-composition ~ 26 — isotherms. Also, it was found that increased annealing temperature lead to thicker layer dissolves. For the experiment, a temperature of 425°C was chosen. Titanium hydride samples were produced at a hydridation temperature of best compromise was deemed to be a 30 minute hydridation time. The optimum hydridation process was found to be a 30 minute anneal at 425°C approximately TiD,.7 and a surface TiO, layer 6 nm thick. _ 27 - Backscattering spectrometry (RBS) was performed on the titanium deuteride 2.2.1 Oxygen Resonance for Determination of Oxygen Concentration Without the use of 3.05 MeV ?®O(a,a)!*%O resonance, it is difficult to deter- with or without the resonant condition. ~ 28 — the oxygen signal is [5]: fe(E)]Z'?° cos 67’ HGP? = yoo(E)QQ (2.1) where (2) is the detector solid angle, Q is the integrated charge, o0(£) is the differ- The integrated charge, Q, is obtained by integrating the ion beam current height of the oxygen signal becomes: E) [e(E) |g: compound A,,B,, the stopping cross section factor is (assuming our scattering ~ 29 — geometry): where @r is the sample tilt angle, @p is the scattering (or detector) angle, e4*?™(E) AnB the stopping cross section e4"”™ can be expressed as AnB n A m B where e4 and ¢® are the stopping cross sections for atoms A and B, respectively. These values can be found in tables such as Table VI and Table VII of Ref. 5. For simplicity, but without losing generality, assume 67 = 0; therefore, Z? can be thought of as the stopping cross section factor for an ion scattering where [e] (2.2), we can now solve for y explicitly as a function of deuterium concentration z: NOES + alfa HE os(B) 3 (2.6) — 30 - The heights are determined experimentally and the stopping cross section factors The 3.05 MeV oxygen resonance has a HWHM of ~10 keV [4,6]. However, scattering cross section: {co(En)hess _ Ho’ [e(Er)lo” z t (2.7) where Ep =3.05 MeV, Heo is the peak height of the oxygen signal after sub- To determine the bulk oxygen concentration in the titanium film, an incident —~31- beam energy of 3.077 MeV was used, corresponding to an oxygen resonance at a direct measurement of the height. To calculate the oxygen content of the Ti samples before deuteridation, Eq. 2.6 teridation) and determined precisely when x has been determined. j 8000 T | T T T T T T T T | T T T t T aT T T 16000 —— Spd/Si09/Ti 14000 10000 Counts 8000 6000 4000 2000 oO L i 1 i 1 es eee ee eo Energy (keV) Figure 2.3a 3.08 MeV Hett backscattering spectra of sample Til0 before and | & 500- 4 r / 400+ 4 ~ O 5 - 4 ~ 300 4 m L 4 200+ A 4 L : A “vA 4 100+ obey : ms ° °o fo} ° | DSA A AA 1 _o 1 ] 4 1 Le? YEA o) | I Energy (keV) Figure 2.3b Background subtracted oxygen signals (data points) and Gaussian — 33 — 2.5 Lj T t T mn I y T T T T T T T t 1 lj T 2.0 1.5 1.0 Oxugen Content y (atZ) 0.5 T PTF f T TT rT T T T ] ¥ T T T T T 7T T T 0 4 | L | L ‘ons 4 1 | oe ia n L Deuterium Content x (atZ%) Figure 2.4 Oxygen concentration as a function of (assumed) deuterium concen- ~ 34 — Deuterium cannot be directly detected by He ion backscattering since its mass From backscattering analysis, it appears that the only significant impurity is and Ti,;_z-yD,Oy after deuteridation, the Ti signal heights will be ro If the same energy, energy calibration, tilt angle, and integrated charge are used for both samples, the ratio of the heights is simply HEP _ 1-2 —y (BIRO (2.9) where [e(E)]7??° can be replaced by its form in Eq. 2.5 to explicitly show its dependence on x and y. Once the heights have been determined experimentally, —~ 35 — y can be found using the formula _ dna {1-2 + ele(ER} a yf? 3 As expected, in this relation y decreases with increasing x. This function is clearly Backscattering spectra using 2 MeV He** were obtained for the same two Ti Figure 2.6 is a plot of Eq. 2.10 using the values for sample Til0, assuming Tig.36Do.6300.01, OF, ignoring the oxygen contamination, TiD; 749.2. — 36 - [ T ] T | T ii ¥ T T T F ] T T ] 300 400 600 800 ‘000 1200 1400 1600 Energy (keV) Figure 2.5 2 MeV RBS spectrum of sample Til0 (tilted 20°) before and after ~37- 2.0 Poo ooo a ee | Eq. 2.10 ‘(Ti signal) TT TF | rT TT Ol Ui Eq. 2.6 fee et EP tt hl Oxygen Content y (atZ) pot i tty Fa Oe eG OD eS Fe 70 45 50 55 60 65 70 75 80 Figure 2.6 Intersection of Eq. 2.6 and Eq. 2.10 which determines oxygen and ~ 38 — X-ray diffraction was used to analyze a Ti sample before and after hydrida- The hydride sample was analyzed instead of the deuteride sample so that a X-ray diffraction was performed using Co Kq (A=1.7902A) and a position sen- may be due to the oxygen contamination. — 39 — 900 1 7 t ey 7 T Temperature °C AY we -300 4 aa nena ~ 0 10 20 30 40 50 s+ eer, wa Figure 2.7 Ti-H phase diagram. The hydrogen concentration as determined by backscattering analysis (6142 at%) is near the border between the fcc 6 phase and ~ 40 — a TU 7000 | 6000, 4 5000 4 4000fF 4 COUNTS 3000 4 2000,- , “| 1000;- 4 0 peace barra terrs bors a tree dere srtisrs te ciitarie teri rtirer trai 20 40 60 80 100 120 Figure 2.8a X-ray spectrum of pure Ti sample before hydridation. 7000 j- 4 6000F 4 5000 #000) ia COUNTS 3000 f|- 4 2000 1000 1} 0 Fae aes Oe OO OD 20 40 60 80 100 120 Figure 2.8b X-ray spectrum of Ti sample after hydridation to TiH,.7. The peaks —~Al— References [1] A. San-Martin and F. D. Manchester, Bull. Alloy Phase Diagrams 8, 30 (1987). [2] T. Smith, Surface Sci. 38, 292 (1973). [3] G. Mezey, J. Gyulai, T. Nagy, E. Kotai. and A. Manuada, Jon Beam Surface [4] J. R. Cameron, Phys. Rev. 90, 839 (1953). [5] W. K. Chu, J. W. Mayer, and M-A. Nicolet, Backscattering Spectrometry (Aca- [6] B. Blanpain, P. Revesz, L. R. Doolittle, K. H. Purser, and J. W. Mayer, Nucl. [7] J. F. Ziegler and Y. K. Chu, J. Appl. Phys. 47, 2239 (1976). [8] J. Ballon, V. Comparat, and J. Pouxe, Nucl. Instrum. Methods 217, 213 (1983). [9] R. L. Crane and S. C. Chattoraj, J. Less-Common Met. 25, 225 (1971). _~ 42 — EXPERIMENTAL PROCEDURES AND RESULTS The concept of the experiment is to irradiate a sample of titanium deuteride Therefore, the neutron detector was not used. 3.1 Experimental Setup An Accelerators Incorporated 400MPR (400kV) ion implanter with a hot cath- target. A bias of +275 V is applied to the target holder for secondary-electron ~ 43 — ‘SUOTJVIPCII UOT JO} pasn Jazue[dury UOT Y_INOOP Jo oeUIayDS TE oansiq ajodnapen> a2INOg Uo] ajodnapenty ol yeqozn0y 2 ; a8eis pub 101294}9] 09 ~ 44 — suppression. The ion dose is measured by integrating the ion current hitting the for sample cooling. An Ortec silicon surface barrier detector with an active area of 0.25 cm? was multichannel analyzer (MCA). The entire detection system was calibrated by placing the detector into the be 5.463 keV per channel with an offset of 23.345 keV. The detector-sample geometry for the fusion experiment is shown in Figure 3.2. be rotated to choose between the six possible positions. The 1.2 x 1.2 cm sample —45 — Incident Beam Side View Incident Beam Top View Figure 3.2 Top and side views of detector-sample geometry. Sample — 46 — was positioned so that the center of the sample was on the beamline axis, with the normal resulting in a 129.6° angle from the incident beam direction. The detector solid angle was calculated as accurately as possible because the 44.1+1.0 mSr for the second detector position. It was necessary to place a filter between the sample and the detector to prevent which could overlap with the *He and T signals and cause noise in the detector that ~47 - could affect the shape of all the peaks. The optimum filter thickness is one which energy, the maximum energy of a sputtered deuteron was approximately 90 keV. Two different filters were used during the course of the experiment. The first backscattered particles. The second filter was a thin window of (LPCVD) SisN, in a (Si) substrate, through the filter is ~10 keV, which is significantly less than the system resolution, — 48 — and much lower than the energy necessary to be counted by the MCA (due to occurred during ion irradiation. 3.2 Experimental Procedures Two sets of experiments were performed: one with the thick Al foil filter, experiment and later measuring the dose by backscattering spectrometry. Each titanium deuteride sample was loaded onto the target holder along with of 1.0 x 10/° ions/cm’. After the first calibration, the titanium deuteride sample —~ 49 — was moved into place. Windows (regions of channels) were set up on the MCA layer had been sputtered away). After the irradiation of the titanium deuteride sample was completed, the charge, and the fusion yield was calculated for each irradiation. In all, twelve irradiations were performed on seven TiD,.7 samples. Table 3.1 first to minimize the effect of the previous irradiations on the subsequent ones. —~50- Table 3.1 Ion Irradiations performed on each TiD,.7 sample. Sample Jon Energy Dose Duration Filter Two types of measurements were made to determine the background spectrum. The second type of measurement was to take a spectrum during the irradiation Therefore, the ion irradiation itself did not appear to contribute to the background. —~51-— 25 a TT TT a a 20 15 Counts 10 T TT TT T ! T mT] T T TT | TT TT pa pe | a t Plt Pt qT T T T @} Sit aR Lu 1 |e on aon 6 | t 1 1 1 | J a | | 1 [a wae | ! 4 {tt Energy (keV) Figure 3.3a Background spectrum taken with no beam and no TiD,.7 sample over 3 m1 T7 i a Energy (keV) Total ion dose = 6.0x10?® ions over a duration of 75 minutes. Background count — 52 — 3.3. Experimental Results 3.3.1 Al Filter Results Spectra obtained using the 5 wm Al filter contained two broad peaks with The region between the proton and triton peaks contains a uniform background The information obtained by recording the ion dose, proton counts, and tri- ton counts (within their respective windows) at five minute intervals can best be ~ 53 - 400 OO OD 350 reitrirritirir triste rrr tr pr ta NO 8) pis to poh a S00 1000 1500 2000 2500 3000 3500 oO Figure 3.4 Spectrum obtained by irradiating TiD,.7 with 5.12x 101° 400 keV Artt ~54—- conveyed in graphic form. Figure 3.5 contains the recorded values for the case of the sample composition). In two of the five irradiations there was a significant drop in the number of pro- from titanium [2,3] do not explain the results observed in this experiment. — 55 —- Dose Dose Rate 9) SO 100 150 200 250 300 0 50 100 150 200 250 300 & r 1 2 f 1 i) 1.0 2.0 3.0 4.0 5.0 fe) 1.0 2.0 3.0 4.0 5.0 Ion Dose (10! ions/cm?) lon Dose (10!§ jons/cm?) 10000 ~~] a a ee 0 1.0 2.0 3.0 4.0 5.0 {e) 1.0 2.0 3.0 4.0 5.0 Ion Dose (10'® ions/cm?) Ion Dose (10'® ions/cm?) Figure 3.5 Record of ion dose and proton and triton counts taken during 400 keV —~ 56 — The fusion yield (fusion events per incident ion) for each irradiation was calculated using the formula (3.1) where Y is the fusion yield, Yq-z is the detected fusion yield (i.e., fusion events In calculating the detected fusion yield (Yae1), only the proton peak was con- Table 3.2. ~57- Table 3.2 Experimental fusion yields for irradiations using the 54m (1.35 mg/cm?) Ion Energy Dose Proton Counts Fusion Yield 3.3.2 Si; N4 Filter Results The spectra obtained using the thin Si3N4 filter differed from those obtained The spectrum obtained during irradiation with 500 keV Xet+ (which is typical Of all the irradiations with the Si3N, filter, only the 150 keV Art and 300 keV Xet irradiations displayed a decrease in the detected fusion yield over the course of ~ 58 — j ele) T TT T | li T T T ] T T t T J T T qT T T T T T T T T T T roy t T T T 80 o LM. a phan be | aA soe tA atau hy i Li Energy (keV) He? T ne) —_—-—~ ee ee [oy Counts t ] T er es Figure 3.6 Spectrum obtained by irradiating TiD;.7 with 1.53x107® 500 keV of 50.8 mSr. ~ 59 — a 2.0 Hose Rote Figure 3.7 Record of ion dose and proton. triton, and *He counts taken during ~ 60 - the irradiation. It is suspected that the detected fusion yield of the 200 keV Xet In calculating the detected fusion yield (Ya.4), again, only the proton peak yields obtained using the Al filter, in figure 3.8. ~61- Table 3.3 Experimental fusion yields for irradiations using a 540 nm (190 ug/cm?) Ion Energy Dose Proton Counts Fusion Yield Ar 600 1.95 x 1076 15346 (1.92+0.20) x 1071° ~ 62 — EF o AI filter : [ A SigN, filter a 4 -10]. ° | re E — AC a “ E 5 A 4 Oo 7 4 7 e107 b ° L = > E _ be : ° -12| 0% rs | 510 “Fe E LL F ¢ 7 -i3{ a (0 "E 4 : 10°14 I Ll | L | i ! i | i { | 100 200 300 400 500 600 Ton Energy (keV) Figure 3.8 Experimental fusion yields for Ar and Xe irradiation of TiD,.7 using ~ 63 — References [1] R. C. Weast, ed., CRC Handbook of Chemistry and Physics 59 (CRC Press, [2] M. Schluckebier, Th. Pfeiffer, K. Muskalla, W. Schmilling, and D. Kamke, [3] M. Schluckebier, Th. Pfeiffer, K. Muskalla, W. Schmiilling, and D. Kamke, [4] A. Krauss, H. W. Becker, H. P. Trautvetter, and C. Rolfs, Nucl. Phys. A 465, ~ 64 - BINARY COLLISION CASCADE MODEL OF FUSION YIELD 4.1 Introduction To identify the processes which cause the fusion events during ion irradiation, Given that it is the collision cascade process that is to be modelled, there are written such a code for the calculation of ion ranges and energy deposition profiles, ~ 65 — which could have been modified (with only some small difficulties) to include the I have used two analytical methods for calculating the fusion yield. The fusion will be discussed briefly in chapter 5. 4.2 Representation of the Collision Cascade As the incident ion penetrates the target material, it transfers its energy to on. Each atom involved in the collision cascade can be labelled by starting with ~ 66 — the incident ion and listing the atoms from each generation leading directly to the dent ion is found by summing the fusion yields of each type of chain: Yxe = Yxepp + Yxetipp + Yxeppp + Yxetitipp + Yxetippp + ..-, (4.1) where Yx¢ is the total fusion yield, and Yx.... is the fusion yield for the chain Xe---. If the fusion yield for a chain did not decrease with the number of intermediate ~ 67 -~ collisions, the sum would be over a very large number of chains. However, collisions intermediate collision can increase the fusion yield of the chain, but, for all others, Yxespp > Yxesspp , Yxex/epp , (4.2) where © and D! are any intermediate chains of collisions. So, if the contribution from other chains are negligible. 4.3 Calculation of the Fusion Yield of a Chain To calculate the fusion yield for a given chain, one starts with the D—D fusion yield Ypipp(E7;) for the chain segment Ti-D-D is calculated as a function of the ~ 68 — Given a deuteron with energy Ep (in the laboratory frame) in a titanium deuteride sample, the fusion yield, Ypp(Ep), is [5] 0 Ep where z is the path length of the deuteron, R is its range, np and nq; are, respec- Given a Ti atom with energy E7;, the fusion yield for the chain segment Ti-D-D before it comes to rest is given by _ Pri do(E,U) dE where np is the atomic fraction of deuterons in the target, do(E,U)/dU is the differential scattering cross section for a Ti atom of energy E to transfer an energy — 69 — U to a deuteron and eq; is the stopping cross section for Ti in TiD,.7. The fusion Et; is Umaz( Eri) Br dE pimpk do(E,Up) (4.5) where Umaz(Evi) = yrvi,p Eri = (4Mq; Mp /(Mri +Mp)) Er; is the maximum energy Note that Ypipp is a function of the fusion yield of the next smaller chain to the form E E Yao...DD(E) = m ff 0 €a(La) Jo (4.6) where a,b can be Ti, D, or the irradiating ion, 7, is the atomic fraction of atom b in To continue the calculation of the fusion yield for the chain Xe-Ti-Ti-D-D, all other chains are calculated in a similar manner. ~70- To calculate the values of the integrals in Eqs. 4.3 and 4.6, the following func- The D(d,p)T fusion cross section is given by [6] S(E) .-o/'? os(E) = E ’ (4.7) where E is the center of mass energy, b=31.39 keV'/*, and S(E) is a polynomial scattering cross section is of the Lindhard form [2] do(E, U) T 2 ~™ 1—my\q —1/q ce where a is the Firsov screening length [7], y is the maximum fraction of energy Because of the complexity of the functional forms of the parameters above, an analytical solution to Eqs. 4.3 and 4.6 is not possible. Therefore, the integrals must ~71-— then becomes “. 0 (tAE/2) Ypp(Ep) = Ypp(nAE) = np » =pGAE) AE Similarly, Eq. 4.6 becomes do(thE,jAU)| AUAE Yoo...DD(E) = Yas.. pp(nAB) =n 5 sy. .Dp(jAU) irate dU €a(iAE) where AU=17, ,AE/m,, where m; is an integer. This choice of AU is made to To calculate the total fusion yield for a given ion (for example, Xe) with an Next, D, Ti, and Xe are added to the front of each of the two chain segments second-generation recoils (Yxeppp and Yxeripp) have been calculated. —~ 72 — To calculate the fusion yields for the next higher generation, D, Ti, and Xe are The FORTRAN program used to calculate the fusion yields of the first three 100 minutes. 4.5 Results and Comparison to Experiment The theoretical calculations of the total fusion yield did not depend strongly the fusion yields decreased with increasing generation. For both Ar and Xe, the fusion yield increases with increasing energy, with the increase being fastest at low energies and slowing at higher energies. The fusion ~ 73 - yields appear to have a behavior similar to that of the D—-D fusion cross section. fusion cross sections. 4.5.1 Model Results for Xe Irradiation The most significant contributions to the total fusion yield for Xe irradiation It is interesting to note that for Xe energies of less than 115 keV the fusion yield be transferred from the Xe to the deuteron through the Ti than can be transferred — 74- 10°9 g——>.—_— rs Tom 107193 Chain Fusion Yield xe-D-0-0-D Xe Energy (keV) 1072! fi 4 ] Figure 4.1a Theoretical fusion yields for the first three generations of recoils for 10° it va siuul Jott itis ie) ho Xe-Ti-Ti-b-p TT TTT jamananatt T TTY 1 Louul Fraction of Tota! Fusion Yield Litt 10°86 100 200 300 400 S00 600 Figure 4.1b The relative contributions (>107°) to the total fusion yield for the —~ 75 — by a direct Xe—D collision (i.e., 7xe,Ti X YTi,D > Yxe,p)- Higher energy deuterons is returned (i.e., Yxepp > YxeTipp).- In general, in order for the addition of an intermediate collision to increase increase will be most pronounced at low energies. For the general case of irradiating material MD, with ion J, it is possible to transfer over that for direct Xe—D collisions (from 5.95% to 15.4%). For the case ~ 76 - of Xe irradiation of Ti-deuteride, the maximum energy transferred by Xe-Ti-D is 2.0 times higher than that for Xe-D. 4.5.2 Model Results for Ar Irradiation In the case of Ar irradiation, the total fusion yield is dominated by the Ar-D—D highest fusion yield from a fourth generation recoil chain (Ya;rTititipp )- Although the mass of Ti is greater than that of Ar, which indicates that it 16%. 1071! Chain Fusion Yield 300 400 900 600 100 200 Figure 4.2a Theoretical fusion yields for the first three generations of recoils for T T T T T I T T T Z] 100 200 300 400 500 600 Figure 4.2b The relative contributions (>10~°) to the total fusion yield for the — 7&8 - 4.5.3 Comparison of Model with Experiment The theoretical fusion yields are quite close to the experimental yields for both values are listed in Table 4.2. The experimental fusion yields are in excellent agreement with those expected heavy ion irradiation. Yield Fusion Figure 4.3a Comparison of theoretical fusion yields for six different interatomic TiD,.7. Fusion Yield Figure 4.3b Comparison of theoretical fusion yields for six different interatomic TiD,.7. 1Q710 197!) 1o71 —~79 - PrP rrr yp rrr pry rrr rp rp rrr pr rr pr prt ys Ar rerererrry to a tl ToT TT ETT YT ap cherpisxytijprirititprrtirietrrias tirizpr tirir tii ri tii | 150 200 250 300 350 400 450 500 550 600 a a a De a xe pop itl T PVerryy rivisitl re rool ba pe to a a 200 250 300 350 400 450 500 —g0- -9 Ion Energy (keV) Figure 4.4 Comparison of theoretical (lines) and experimental (data points) fusion —~81-— Table 4.1 Reduced x? values for theoretical fits to the experimental fusion cross Reduced y? Potential Xe Ar Total Table 4.2 Experimental fusion yields and theoretical fusion yields calculated using TiDj.7. lon Energy Experimental Fusion Yield Theoretical Fusion Yield ~— &2- References [1] J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions [2] P. D. Townsend, J. C. Kelly, and N. E. W. Hartley, Jon Implantation, Sputtering [3] J. P. Biersack and L G. Haggmark, Nucl. Instrum. Methods 174, 257 (1980). [4] J. P. Biersack and W. Eckstien, Appl. Phys. A 34, 73 (1984). [5] C. Carraro, B. Q. Chen, S. Schramm, and S. E. Koonin, Phys. Rev. A 42, 1379 (6] A. Krauss, H. W. Becker, H. P. Trautvetter, and C. Rolfs, Nucl. Phys. A 465, [7] J. P. Biersack, E. Ernst, A. Monge, and S. Roth, Tables of Electronic and [3] Ik. B. Winterbon, Rad. Effects 13, 215 (1972). [9] H. H. Anderson and J. F. Ziegler, Hydrogen Stopping Powers and Ranges in ~ 83 — DOPPLER ANALYSIS OF PEAK SHAPES During the irradiations utilizing the Si3N, filter, it became apparent that the The shape of the fusion product signals is a function of detector resolution, en- analysis is focussed on the proton signal. —~ 84 - 5.1 Processes Affecting Peak Shape There are four factors that effect the detected energy of the fusion products. The energy loss of the fusion products on the outward path through the ti- From the detector-sample geometry, it is calculated that the distribution of in- cident angles for fusion products entering the detector through the filter is roughly Gaussian, with a mean value of 9° and a FWHM of 11°. Given this angular —~ 85 Given energy distributions of fusion products exiting the sample surface, the butions with the detected energy loss distributions in Table 5.1. Table 5.1 Energy loss distributions for mono-energetic beams of fusion products Mean Filter Filter+Detector 5.2 Modeling the Deuteron Energy Spectrum As discussed in Chapter 4, when an energetic ion J enters the titanium deuteride Those chains resulting in fusion events must end in a D-D collision. For all cases — 86 — 350 TTT a ne ee es ee eee ne) ——_—— pope tire rt tipper tip ei tip ey ler ti yy PET pT err ryprrrryprrrryprrrrprr rt rrr u N 0 S00 1000 1500 2000 2500 3000 3500 je) Figure 5.1 Comparison of theoretical and experimental fusion spectra for ~87- studied in this experiment, the fusion yield is adequately described by In Chapter 4, these yields were calculated by starting with Ypp and working back- In this section, the fusion yield will be calculated by starting with the incident Given an incident Xe ion with energy Exe, the energy distribution of titanium atoms produced by Xe—Ti collisions is given by Exe do(E,U) dE where vxeqi(U) is the number of Ti atoms per unit energy with energy U, 77; is the section for Xe-Ti collisions, and ex, is the stopping cross section for Xe in TiD, 7. — 88 — Given the distribution vxe7; of primary Ti recoils, the second generation of Ti energy and integrated over all primary recoil Ti energies do(E,U) dE Evi, max Ey where Eq; max i8 YxeTiExe. This formula can be generalized for calculation of n“* generation recoil distributions from (n — 1)" distributions: E E a@,max 1 do(E, U) dE where a,b can be Ti or D, 7 is the atomic fraction of atom b, da/dU differential The number of fusion events per unit energy occurring with a penultimate Ep,max of fusion events per unit energy over all energies Ep, max ~ 89 — This equation gives exactly the same fusion yield as Eq. 4.6 for the same chain and ion and ion energy. 5.3 Model Results To compute the energy distribution of deuterons at the moment of fusion and Calculations were made for 150, 300, 450, and 600 keV Ar and 200, 300, and The energy distribution for deuterons caused by 600 keV Art* irradiation is ~ 90 — shown in figure 5.2a, and the distribution for 200 keV Xe* irradiation is shown in number of deuterons from the Xe-Ti-D chain dominates. The profiles of fusion yield as a function of deuteron energy at the time of fusion the fusion yield comes from primary recoils in later and later stages of the cascade. The profiles of fusion yield as a function of deuteron energy for all Xe irradi- to the increasing contribution of the Xe-Ti-D-D chain to the total fusion yield. ~ 91 — 10° : v (deuterons/keV) T I T T T T TT Tt T L \ 1 1 4 | 20 40 60 80 100 Figure 5.2a Theoretical deuteron energy distributions for 600 keV Art* irradia- v Cions/keV) 5 10 15 20 25 Figure 5.2b Theoretical deuteron energy distributions for 200 keV Xe? irradiation A a Deuteron Energy (keV) Figure 5.3 Theoretical fusion yield as a function of deuteron energy at the time -— 93 - TTT rrr pr reper errr rrr yp rr er yr rer perry 1.20 Xe 500 keV i 300 keV Fusion Yield (10°'3 events/ion/keV) 1 4 oe ee ee | toi i i i + | oe a oe Deuteron Energy (keV) Figure 5.4a Theoretical fusion yield as a function of deuteron energy at the time 2.5 T T T T T T T T T y 7 T T T i] a T t T T T T T T 2.0 1.5 1.0 0.5 Fusion Yield (107! events/ion/keV) pops Pe Pt tl 0 “5 10 15 20 25 Figure 5.4b Enlarged view of the fusion yield for 200 keV Xe irradiation explicitly ~ 94 — The energy of the proton emitted in the D(d,p)T reaction is 3.02 MeV in the proton CM velocity, the proton lab velocity is the CM frame, and @,m is the velocity of the CM frame relative to the lab frame. For an ion of rest mass my and kinetic energy E, the velocity v is 2 2 The relativistic formula is used to convert between energy and velocity because the 1/2 relativistic correction (0.25% for 3 MeV protons) is greater than the energy width of Given the distribution of deuteron energies (in the lab frame) immediately Since the Doppler shift is dependent on the angle between the proton velocity and the CM velocity, an angular distribution of the CM velocities must be assumed. —~ 95 — This angular distribution lies somewhere between a unidirectional beam directly into closer to the unidirectional than the isotropic angular distribution. Because an accurate accounting of angular distributions as well as energy dis- time of fusion. From a phenomenological viewpoint, the deuterons with the maximum energy the same direction as the incident ions. The lower the deuteron energy, the more ~ 96 — (5.10) (8) = _ (6 — 130°) | | Vin oT) | 20%(T) The energy loss mechanisms resulting in a deuteron energy (T) at the time of (AT or), and nuclear and electronic energy loss of the deuteron before fusion occurs (ATp nucATp,elte), 1.€., Because the electronic energy losses do not result in angular deviation, only The relationship between energy transferred to the deuteron and scattering angle of the deuteron in the lab frame is [5] 4M, M2 = (Mi, + My?“ cos” G= Tmax cos” 6 5 (5.12) _97- to give the scattering angle as a function of the energy transfer T \i? = eoent | ( Tine AT” where AT = Tmax — T is the difference in energy between the maximum energy 6 = cos” (5.13) transfer and the actual energy transfer. Since the relative contributions of the different energy loss terms of Eq. 5.11 are deviation o(T) of the angular distribution is (= = nve(Tmax — =) " i (5.14) a(T) = cos" 7 where nNnuc is the fraction of the difference between Tyax and T due to nuclear Using the deuteron energy distributions calculated in Section 5.3 and angular to give the theoretical detected proton spectrum. For cases in which more than one — 98 - collision chain gives a significant contribution to the fusion yield (such as for Xe each chain will have its own set of angular distributions. 5.5 Comparison with Experiment The transformation described above was performed for the theoretical deuteron For all Ar irradiations, the best fit to the experimental spectra is achieved using Although the precise angular distribution of D-D CM velocities was not com- of those particles upon exiting the titanium deuteride. If a more precise angular —~ 99 — 900K 600 keV Ar = 2700 2800 2900 3000 3100 3200 Energy (keV) Figure 5.5a Comparison of unidirectional (@ = 130°) and distributed angle (with 30 a TT T TT | “TT T T | T T ‘\ T 7 T T T T mf T T qT T } T Tt T T J i 200. keV X / | Model (@ = 1309 4 i }.keV Xe 4 29 [ ; \ as F —_ 1 20 }- , a C b \ 4 Sf a 1 O { ‘ 4 c 15 : Model! | i 4 a | “40% nuclear stopping) . \ 7 ; Experimental Data : 5 4 0 =< i oa Ee ss 2 = Energy (keV) Figure 5.5b Comparison of unidirectional (@ = 130°) and distributed angle (with 40% Nuclear Stopping) models and the experimental proton signal for 200 keV Xet ~ 100 - distribution could be computed, it might be used to extract information about the distribution are most noticeable. ~ 101 - References [1] H. H. Anderson and J. F. Ziegler, Hydrogen Stopping Powers and Ranges in [2] J. F. Ziegler, J. P. Biersack, and U. Littmark, The Stopping and Range of Ions [3] J. P. Biersack, and L. G. Haggmark, Nucl. Instrum. Methods 174, 257 (1980). {4] D. D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (McGraw- (5| J. B. Marion, Classical Dynamics of Particles and Systems, 2"¢ edition (Aca- demic, New York, 1970). ~ 102 - Chapter 6 CONSIDERATIONS ON APPLICATIONS 6.1 Comparison with Existing Techniques As was shown in Chapter 4, the binary collision cascade model quite accu- Currently used methods of hydrogen (and deuterium) profiling include Forward Two FRES methods have been utilized. The first method involves irradiating tons at +45° from the incident beam direction [4]. This method has the drawback — 103 ~ that samples must be self-supporting films thin enough to allow the clean transmis- concentration. SIMS, which mass analyzes ions sputtered from the sample surface during system, none of which can be accurately corrected for. The third method, NRA, which detects backscattered particles with the charac- signal. The advantages of determining deuterium concentrations using the method of the present work, compared to the above methods, are (1) absolute concentrations ~ 104 ~ are measured (no standard is necessary), (2) low energy ions (~500 keV) can be depth profiling capability, and (3) deuterium must be substituted for hydrogen. 6.2 Optimum Parameters for Measuring Deuterium Concentration To optimize the utility of heavy-ion-induced fusion as a method of determining From Fig. 4.4, it is clear that increasing the ion energy increases the fusion our implanter, Ar or Ne would be preferable. To minimize the dilution effect of the incident beam, a lighter ion is preferable ~ 105 - ~9 Ion Energy (keV) Figure 6.1 Comparison of theoretical fusion yields for irradiation of TiD;.7 with ~ 106 - over a heavier ion because it penetrates farther into the sample and has a smaller to a lower energy one. Finally, the effect of the matrix element M containing the deuterium must be error involved in ignoring all other chains is negligible. For titanium deuteride, considering fusion yields, dilution effect, simplicity of calculation, and available beam current on our implanter, Ne is the optimum ion for — 107 - energies below 500 keV, and Ar is the optimum ion for energies above 500 keV. Fig- irradiation preferable to Ne irradiation. Since there is virtually no background in the region of the proton peak, the range of those for the nuclear reaction analysis methods described above. The model of the binary collision cascade has been shown to accurately pre- surface region of a titanium sample. Further research with this technique may lead ~ 108 - 10°79 E T T T 7 7 T T 1 T T T T q Deuterium Concentration (atZ%) Figure 6.2 Theoretical fusion yields as a function of deuterium concentration for — 109 - to the development of a method of analysis suitable for use on ion implanters with an energy range of a few hundred kV. -110- References [1] J. F. Ziegler, C. P. Wu, P. Williams, C. W. White, B. Terreault, B. M. U. [2] P. D. Townsend, J. C. Kelly, and N. E. W. Hartley, Jon Implantation, Sputtering [3] W. K. Chu, J. W. Mayer, and M-A. Nicolet, Backscattering Spectrometry (Aca- [4] B. L. Cohen, C. L. Fink, and J. D. Degnan, J. Appl. Phys. 43, 19 (1972). [5] T. T. Bardin, J. G. Pronko, and A. Joshi, Thin Solid Films 119, 429 (1984). [6] B. Terreault, J. G. Martel, R. G. St-Jacques, and J. L’Ecuyer, J Vac. Sci. [7] D. A. Leich and T. A. Tombrello, Nucl. Instrum. Methods 108, 67 (1973). [8] E. Ligeon and A. Guivare’h, Rad Eff. 22, 101 (1974). [9] P.P. Pronko and J. G. Pronko, Phys. Rev. B 9, 2870 (1974). —111- Appendix 1 FABRICATION OF THIN SIZ;N, FILTERS The purpose of the Si3N, filter is to block sputtered particles and backscattered The detector is a silicon surface-barrier detector with a diameter of 16.75 mm. and the active area of the detector. The fabrication procedure began with a 4” (100) Si wafer coated on both sides and removed, leaving bare Si;N, (Fig. Al.1b). The exposed back-side Siz;N, was — 112 - removed using a SFg RF plasma etch. After plasma etching, the photoresist layer The exposed silicon was etched using an anisotropic silicon etch (EDP), which The Si3N4 layer was characterized using 2 MeV Het* backscattering spectrom- a specific gravity of 3.44 g/cm’. — 113 - 4” (100) Si wafer patterned with 18 filters Photoresist (B) — (100) Si beers eae e eee ee ep rae (C) SisN4 0.55ym < (100) Si 7 . = . (D) ys SigN4 0.55 pm V \ / V (100)Si E) _ — /. 8.0 mm / SisN4 filter Figure A1l.1 Procedure for fabricating thin SisN, filters. -~114- Appendix 2 FORTRAN PROGRAM USED TO CALCULATE This FORTRAN program was used to calculate the theoretical fusion yields This version of the program is not designed for optimum speed, but to give branches into a single step. Run time of this version on our VAX is approximately 2.5 hours. eaqnaaaqannnnaann aagnan 110 -—115- program fusion This algorithm calculates the D(d,p)T fusion yield for heavy ion first 3 generations of recoils, plus one of the fourth generation. The fusion yield of all chains involving the incident ion are KR KKK KKK KKK KK KKK KEK RK KK KK KKK KKK KKK KKK KKK KKK KKK KKK KKK KKKKKKKKKKKKK * Note: To modify the incident ion simply modify Ma(3) and 2(3) * modify the coefficients for the electronic stopping of deuter- KKKK EK KKK KKK KKK KK KE KKK KKK KKK KK KKK KK KKK KKK KKK KK KK KKK KKK KK KK KK KKK KKEK real*8 Ma(3),2(3),10(3),pi,a0,e2,Me + Yiddd (2000) , Yimdd (2000) , Yadddd (2000) , Ymddd (2000), + Ydmdd (2000) , Ymmdd (2000) , Yidddd (2000) , Yimddd (2000), + Yidmdd (2000) , Yimmdd (2000) , Ymmmdd (2000) , Yimmmdd (2000), real*8 E,E0,E d max,E_m max,stp character fileout*30, file*22,lab1*4 real*8 conv_nl1,conv n2,conv_el1,conv_e2,conv_e3,conv_e4 real*8 xd,a,gamma ~ ~ common /infol/ xd,a(3,2),conv_n1(3,2),conv_n2(3,2),conv_e1(3,2), integer ipot,loop common /info2/ delE(3),atfrac(3),ipot, loop real*8 lambda,m,q common /coef/ lambda (6) ,m(6),q(6) RAKKKKK Setup of Parameters for dscs KAKK KKK K lambda(1) = 1.70 ! Thomas-Fermi-Sommerfeld q({1) = 0.588 lambda(2) = 2.37 ! Bohr m(2) = 0.103 q(2) = 0.570 lambda(3) = 2.92 ! Lenz-Jensen m(3) = 0.191 q(3) = 0.512 lambda(4) = 0.625 ! Lindhard (c*2 = 1.8) q(4) = 1.24 lambda(5) = 0.879 ! Lindhard (c*2 = 3) q(5) = 1.24 lambda(6) = 3.07 ! Moliere m(6) = 0.216 q(6) = 0.530 KRKKKAKKAEKKKK Tnput Initial Parameters ***KKKKKEKKKKKK format (/,' Enter [1] for Ar or [2] for Xe irradiation: ',$) format(' Enter the Interatomic Potential Number: ',$) format (' Enter the amount of Dueterium in the film TilDx: ',$) AaAAN 200 aAagaAaNAANANN —116- read(5,*) ion write (6,120) read(5,*) EO EO=E0*1000.00 ! Convert Energy to eV read(5,*) ipot write (6,140) read(5,*) xd call labels (labl,ilen2) RXKKKKKKAKKK Setup of the Common Variables *****x*xxkK** **k* constants ** Loop=1000 ! The number of divisions in the distributions a0=0.529172 ! Bohr radius in Angstroms e2=14.3996 ! Electron charge squared in units of keV Angstroms ** target and ion properties ** — atfrac(1)=1.0/(1.0+xd) ! Metal atomic fraction atfrac (2) =xd/ (1.0+xd) ! Deuterium atomic fraction Ma (2) =2.01594 ! Mass (amu) Z(3)=18.0 ! Irrad. Ion (Ar) - Atomic Number if (ion .eq. 2) 2(3)=54.0! Irrad. Ion (Xe) - Atomic Number if (ion .eq. 2) Ma(3)=131.305 ! Mass (amu) xx interaction parameters ** + ((Z (1) ** (2.0/3.0) 4+Z (5) ** (2.0/3.0) ) **1.5*Ma (i) **0.50) KKKKKKKKKKKKKK Calculation of D-D Yielq@ ***KKKKKKKKKKKK Using iterative Eq. 4.9 of Thesis, where stp = xnucstp(2,delE(2)) + delestp(del1E (2) ) E=float (i) *delE (2) stp = xnucstp(2,E) + delestp(E) AAANDAAN aan 500 —117- Ydd(i) = Ydd(i-1) + atfrac(2)*fcs (E) *delE(2)/stp Calculation of Higher Generation Yields Call a subroutine which uses iterative Eq. 4.10 of thesis call fuse(2,2,Ydd, Yddd) ! D-D-D Yield call fuse(1,2,Ydd, Ymdd) ! M-D-D Yield call fuse (3,2, Ydd, Yidd) ! I-D-D Yield xx Second generation recoils ** call call call KHEKKKKKEK do 500, fuse (2,2, Yada, Yaddd) D-D-D-D Yield Third generation recoils Fourth generation recoils D-M-D-D xx fuse (2,1, Ymdd, Ydmdd) Yield fuse (3,2, Ydddd, Yidddd) {or Yield Calculation of Total Fusion Yield ****x**kx*kxx i=1, loop continue KREKKKKKKKKKEKEKKKKKKKK call Store RESULTS KKK KKKKKKKKKKKKKK KKK titler('Idd',3,labl,ilen2, fileout) * Ion-D-D Fusion Yield ') ' Ton-D-D-D Fusion Yield ry ' Ion-D~D-D-D Fusion Yield ') ' Ion-Ti-D-D Fusion Yield ry) ' Ton-Ti-Ti-D-D Fusion Yield ') ' Ton-Ti-Ti-Ti-D-D Fusion Yield') ' Ton-Ti-D-D-D Fusion Yield ') ' Ton-D-Ti-D-D Fusion Yield ') ~118- + ' Total Fusion Yield ') 1000 continue aqAaaqaaqaqagnaanaqa a AQAQAQAQARANAAANANANAN A 100 200 end function xnucstp (ion, energy) * This gives the nuclear stopping power (epsilon_n) in units of * real*8 epsi_m,epsi_d,Sn_m, Sn_d, energy, xnucstp real*8 conv_ni,conv_n2,conv_el,conv_e2,conv_e3,conv_e4 real*8 xd,a,gamma common /infol/ xd,a(3,2),conv_n1(3,2),conv_n2(3,2),conv_e1(3,2), Sn_m=conv_n2 (ion, 1) *log(epsi_m)/(epsi_m-(epsi_m) ** (-0.50)) Sn_d =conv_n2 (ion, 2)*log(epsi_d)/(epsi_d-(epsi_d) **(-0.50)) end KARR KKK KKK KK KKK KKK KKK KKK KKK KKK KKK KKK KK KKK KK KKK KKK KAKKKKKKKKKKKKKEKKK function elestp (ion, energy) * This gives the electronic stopping power (epsilon_e) in units * real*8 S1(2),Sb(2),Se(2),epsi_b, energy,elestp AaANQAANN A 200 300 aaqncnaaaaaa a AAAANAN Aa — 119 - KK KKK KKK KK KKK KK KKK KKK KK KK KKK KKK KR KKK KKK KK KK KKK KKK KK KKK KKK KKKKKKEK x This gives the electronic stopping power (epsilon_e) in units * real*8 Se d,Sl1_d,Sh_d,Se_ti,Sl_ti,Sh_ti,E,energy, delestp Input Parameter i = number of interatomic pontential used + te ee He + + + 4 aqananaaqgaanna aaa aan 100 aan 200 300 — 120- * Rolfs, Nuclear Physics A 465 (1987) 150. * b=31.39 ! units of keV*1/2 S0=5.290E-07 ! units of keV Angstrom*2 S1=1.900E-10 ! units of Angstrom*2 $2=3.840E-11 ! units of Angstrom*2/keV E_cm=0.500* (E_lab/1000.0) ! E_cm in keV, E_ lab in ev return end KKK KK KKK KE KKK KKKEKKKKKKK KKK KKK KK KK RK kk kkk kk kk dk kok Calculation of fusion yield Yout given fusion yield Yin Yin = Yb...D Yout = Yab...D stp = epsilon_a subroutine fuse(ion, itarg, Yin, Yout) real*8 Yin(2000) , Yout (2000) ,delU,U,E,sum, stp real*8 conv_ni,conv_n2,conv_el,conv_e2,conv_e3,conv_e4 real*8 xd,a,gamma ~ common /infol/ xd,a(3,2),conv_ni(3,2),conv_n2(3,2),conv_e1(3,2), integer ipot, loop common /info2/ delE(3),atfrac(3),ipot, loop KAKKKKKKKKEKK Calculation of Yab...DD(1) ****kkKkKKHKK HK m = int (delE (ion) *gamma (ion, itarg) /delE (itarg))+1 U=float (3) *delU nl = int (U/delE (itarg)+0.50) sum = sum + Yin(n1)*dscs(ion,delE(ion),itarg,U, ipot) *kEKKEKK Therative Calculation of Yab...DD(i) ****xxxxx do 300 i=2, loop aANAgAANN 20 100 200 AAgNAANANA ANMQAAAAANAN -—121- return end KK IK KKK KKK IK KK IK KKK KKK KI KKK KKK KKK KEK KIRK KK KKK KAKKKEKKKKKEK KKK KEKE KEK RK KKK KEK KKK KKK KEKE KKK KE KKK KEK KEK KKK KKK KK KKK KK KK KK KKK This section collects and determines the length ofa subroutine labels (labl,ilen) character xchar*4,labl*4 write (6,10) format (' Enter a label up to 4 characters long: ',$) read(5,20) xchar format (A4) key=0 do 100, i=1,4 continue i=5 continue ilen=i-ibeg if (key .eq. 0) ilen=0 labl(1:ilen)=xchar (ibeg:i-1) if (ilen .it. 4) labl(ilen+1:4)=' ' return end KR KEKE KK KE KKK KKK KR KK KE KK KKK KKK KK KKK KKK KEKE KK KKK KKKKKKKKAKKKKKK KEK KKK KEK KK EKER KE KK KKK EK KEKE KK KEK KKK KKK KKKKKKKEKEKKKKE KK KKK This section appends the identifying label and the exten- Subroutine titler(file,ilenl,labl,ilen2, fileout) fileout (1:ilen1)=file(i:ileni) fileout (ileni+1:ileni+tilen2)=labl (1:ilen2) fileout (ilenl+ilen2+1:itot)='.fit! if (itot .1it. 30) fileout (itot+1:30)=' return end KKEKKKEKKKE KEK KK KKK KKK KKK KKK KKK KEKE KEK KKK KEKE KKK KKK KK KKKKKKKKEK KREKK KKK KK KKK KKK KKK KKK KK KKK KK KKK KKK KKK KKK KKK KKK KKKKK KKK KKK This section stores "thick target" fusion yield vs energy subroutine stofus (fileout, ion, Y, label) character fileout*30, label*30 real*8 delE,atfrac integer ipot,loop common /info2/ delE(3),atfrac(3),ipot, loop 100 1000 1050 — 122 - write (1,1010) label write (1,1020) write (1,1030) write (1,1040) do 100 i=1,loop/10 continue close (unit=1) write(6,1000) fileout format (' Fusion Profile saved in file : ',A30) format (' ',A30) format(' Ion Energy (keV)') format (' Fusion Yield') format (12X%,'9',11X,'1',/,' 0.0000000000000000E+00', /, + 11x, '0',/,11X,'0"') format (1X, 1PG14.6,',',1iPG14.6,',',1PG14.6) return end plot label ! fitting parameters (connect points)
V(r) = + r>R,
Vauc r
tial, Vauc is the (attractive) nuclear potential. Z; and Z2 are the atomic numbers of
the interacting particles, and | is the orbital angular momentum quantum number.
The form of this potential is shown in figure 1.1. The potential barrier reaches its
maximum height at r=R. For the D—-D reaction, the peak coulomb barrier is ap-
proximately 0.4 MeV and the peak centrifugal barrier is approximately 0, 3.4 MeV,
and 10.0 MeV for the states /=0,1,2, respectively, at r=3.5 fm. It can be seen that
negative potential is due to the strong nuclear force. For r > R the coulomb
and centrifugal potentials present a barrier which must be penetrated for a reaction
to occur (taken from [24]).
higher orbital angular momentum states from participating in the reaction for low
energy deuterons, resulting in nearly isotropic angular distributions of the reaction
products at low energies.
that of the coulomb barrier. Therefore, for fusion to occur, the deuterons must
tunnel through the potential barrier. The reaction cross section for this case is of
is the relative velocity of the particles, S(E) is the astrophysical S$ factor, and
b=31.29 2, Zopil? keV}/2,, where pis the reduced mass in units of amu. The S factor
is normally a slowly varying function of energy away from the vicinity of resonances.
The exact forms of the nuclear wave functions and the interaction potential are not
known well enough to determine S(E), and thus o(E), from theoretical calculations.
Therefore, experimentally normalized cross sections are relied upon in the present
work.
ergies of 2.98 to 162.5 keV by irradiating a deuteron gas target with energetic
deuterons [25] and have been studied at energies above 10 keV by many authors.
Absolute cross sections and angular distributions have been reported for both re-
actions. The values of S(E) calculated from the measured cross sections [25] are
shown in figure 1.2. These values are from angle integrated data. The angular
distributions of the reaction products are shown in figure 1.3. As expected, because
of the relatively large centrifugal barrier, the angular distribution is nearly isotropic
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ENERGY E,,,(keV)
(b) D(dn)*He. The solid curves are the results of polynomial fits to the data
for Eom <120 keV (taken from [25]).
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D(d,n)*He reactions. The solid curves through the data. points are the results of x?
analysis using even Legendre polynomials (taken from [25]).
1.5 to 3 keV by irradiating thin foils of TiD2 with energetic deuterons [26]. The
cross sections obtained are in good agreement with those calculated using S(£)
determined from the experiment above. Thus, fusion cross sections for deuterium
in gaseous form and in solids (where it is possible that electron shielding could affect
the cross section) are roughly equivalent.
center-of-mass energy at which fusion occurred was estimated to be less than 25 keV
for all irradiations. Therefore, the assumption of an isotropic distribution of fusion
products is a relatively good one. In addition, the angle at which fusion products
were detected (130° in the lab frame) was near the angle of average fusion yield
(125° in the center-of-mass frame), resulting in a deviation of less than 4% from
the angle integrated cross section for the highest energy deuterons produced in this
Lett. 50, 1485 (1987).
Lett. 45, 185 (1984).
(1987).
4, 579 (1989).
Lett. 46, 610 (1985).
54, 413 (1989).
{9] J. J. Reilly, Z. Phys. Chem. NF 117, 155 (1979).
10] M. Fleischmann and S. Pons, J. Electroanal. Chem. 261, 301 (1989).
S. F. Taylor, and J. Rafelski, Nature 338, 737 (1989).
S. Podda, and F. Scaramuzzi, Europhys. Lett. 9, 221 (1989).
1989 (unpublished report).
and their Applications (Academic, London, 1976).
47 (Springer-Verlag, Berlin, 1981).
Nuclear Stopping Powers and Energy Straggling for Low Energy Ions (Hahn-
Meitner-Institut, Berlin, 1975) pp. 3-5.
Hill, New York, 1968), Ch. 4.
150 (1987).
Chapter 2
quirements of the experiment. Since the fusion yield from ion irradiation was ex-
pected to be quite small, possibly at the limit of detectability, the samples needed
to be designed to maximize the number of fusion events produced. In terms of com-
position, this meant maximizing the deuterium concentration. (A collision between
two deuterons is necessary to create a fusion event; therefore, the fusion yield varies
quadratically with deuterium concentration.) In terms of sample configuration, the
TiD layer had to be thick enough so that the entire collision cascade caused by the
ion with the largest projected range would remain entirely within the TiD layer.
This was planned to be 300 keV Art, with a projected range of 200 nm and a range
straggling of 80 nm; therefore, the minimum TiD thickness would be about 300 nm.
Finally, the area of the sample had to be large enough so that the maximum ion
beam current could be applied to it, yet still be able to fit in the hydrogen furnace.
The beam in our ion implanter cannot be focussed to a size smaller than approx-
imately 1 cm square, while the furnace cannot accommodate samples wider than
1.2 cm. Therefore, a sample size of 1.2 cm x 1.2 cm was chosen.
vacuum system pumped with an ion pump. The base pressure of the system was
3 x 10~® Torr, and the pressure remained below 2 x 10~" Torr during evaporation
at a rate of 2 - 2.5 nm/s. The substrate used was a 2 inch (111) Si wafer with a
showed the thickness of the Ti layer to be 325 nm, with a variation of less than 5%
over the entire wafer, Also revealed was a ~1.4 at% oxygen contamination in the
a temperature high enough to allow deuterium to penetrate the surface oxide layer
and for a time long enough for a homogeneous TiD layer to form. The optimum
temperature and deuterium pressure for creating TiD with the highest deuterium
concentration were found by consulting the pressure-composition isotherms for the
Ti-H system (Fig. 2.1) [1]. From the figure, it is clear that, for a given hydrogen
pressure, the hydrogen concentration increases with decreasing temperature. For a
given temperature, the hydrogen concentration increases with increasing pressure.
Therefore, to maximize the hydrogen (or deuterium) concentration, a combination
of low temperature and high pressure must be used. For a composition of TiD2, a
pressure of ~20 ATM is necessary at 500°C, ~2 ATM at 400°C, or ~0.1 ATM at
300°C.
cost of deuterium (~$2 per liter), and safety, a furnace with a static D ambient
(as opposed to one with flowing D) was used for deuteriding of the Ti films. Also,
because of the cost of deuterium, hydrogen (1H) was used initially, until good quality
(part of which is enclosed in a furnace) connected to a metal tube with connections
for introducing hydrogen or deuterium, loading the samples, rough pumping, and
measuring the pressure (Fig. 2.2). The quartz tube is roughly 1 inch in diameter,
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Gauge
Gauge
Pump
samples.
is sealed with a blank flange using a viton O-ring. Copper gaskets were used for
the other three arms of the cross. The lower arm of the cross is used for rough
pumping and venting. The roughing pump used is a rotary-vane mechanical pump
with a pumping speed of 20 ¢/s and ultimate vacuum of 5 mTorr. The upper arm is
used for introducing hydrogen or deuterium. A three-position gas-inlet valve selects
between hydrogen, deuterium, or closed. This arm also contains a thermocouple
pressure gauge for measuring vacuum during roughing. A second gauge, attached
to the sample loading flange, is used for measuring pressures of -30 inches of Hg to
+60 psig during deuteridation. Stainless steel tubing is used between the regulators
on the gas bottles and the gas-inlet valve. The total volume of the system (between
the roughing valve and the gas inlet valve) is approximately 550 ml. The base
pressure of the system is 40 mTorr, and the system is able to maintain a pressure
of under 200 mTorr for 24 hours without being pumped. It will hold a positive
the Ti samples. The boat is attached to a quartz rod, which in turn is attached
to an aluminum housing. The aluminum housing contains an iron roller which can
be manipulated with a magnet from the outside of the system in order to move the
boat in and out of the furnace. A small quartz basket containing 99.8% pure Ti
sponge is placed at the end of the quartz tube. The sponge is used to getter any
oxygen before the samples are moved into the furnace. The purity of the hydrogen
taining Ti sponge was placed at the far end of the quartz tube. Ti samples were
sealed and roughed down to the base pressure. The system was then filled with hy-
drogen (or deuterium) to a pressure of 10 psi above atmospheric pressure (10 psig)
and then roughed to the base pressure again. This purge cycle was repeated 3
times to minimize the residual air content in the system. After the purge cycles,
the system was filled to the desired pressure and the gas inlet valve was closed. At
this point, all valves were closed, and the amount of hydrogen in the system was
maintained for approximately 2 hours in order for the Ti-sponge to getter any
residual oxygen. Next, the temperature was lowered to that desired for the deu-
teridation process and the Ti samples were moved into the furnace and annealed
for the desired time. Finally, the temperature was lowered to 250°C and the sam-
ples were annealed for about 16 hours to form a homogeneous layer. The samples
were removed only after the furnace had reached room temperature so that oxygen
perature, and time. A log of temperature and pressure versus time was kept for
each run. Temperatures of 250, 300, 350, 400, 425, 450, and 500°C were used;
however, only those above 400°C produced a measurable amount of hydridation.
Hydridation times were varied from 30 minutes to 20 hours. The pressure was set
from 20 - 30 psig at room temperature, producing pressures of 15 - 35 psig during
hydridation. As the furnace temperature was raised and lowered, the pressure var-
ied (since it was a closed system). However, only a fraction of the tube volume was
heated, making it difficult to anticipate the pressure for a given furnace tempera-
was made to predict the hydriding pressure from the pressure set at the beginning
of the experiment, rather, the pressure was measured during the experiment. It was
found that the above variation in hydriding pressure did not significantly affect the
ence of a native oxide on the Ti films. The same behavior was exhibited by the Ti
getter. A steady increase in pressure occurred as the furnace was initially heated
up. However, a sharp drop in pressure (~4 psi) occurred as the furnace temperature
rose above ~400°C indicating the absorption of hydrogen by the Ti getter. While
increasing the temperature at ~1°C/min, this sudden drop occurred at 40142°C.
Reference 2 indicates that at approximately 400°C TiO, dissolves into the bulk,
35 psig showed no measurable intake of hydrogen. Also, samples annealed at 425°C
for 30 minutes and then at 250°C for 16 hours contained roughly the same amount
of hydrogen as those annealed only at 425°C for 30 minutes. The only effect of the
250°C anneal was to uniformly distribute the hydrogen throughout the Ti layer.
Therefore, it appears that heat treatment above 400°C does not permanently remove
the barrier to hydrogen absorption, but only removes it during the time the film
temperature exceeds 400°C. This interpretation is consistent with a surface oxide
layer which acts as a barrier to hydrogen absorption below 400°C but is dissolved
H pressure and anneal duration produced TiH films that had decreasing H concen-
surface oxide layers and higher oxygen concentrations in the TiH films. The source
of the oxygen is unclear, but since a getter was used, it may be posited that oxygen
or water vapor are outgassing from the quartz boat and push rod when they and
the samples are first placed into and heated by the furnace. From these results, the
optimum temperature that maximizes the hydrogen concentration and minimizes
the oxygen contamination is located just above the point at which the surface oxide
425°C and a pressure of 35 psig for times of 30, 90, and 180 minutes. Resulting hy-
drogen concentrations increased from TiH;.¢5 to TiHi.s5 with increasing annealing
duration. However, increasing anneal duration also increased surface oxide thickness
and oxygen concentration in the bulk of the film. For example, the surface TiO.
layer thickness was 6 nm after 30 minutes and 15 nm after 180 minutes. Changes in
the 250°C annealing duration after the higher temperature hydridation anneal did
not appear to affect the oxygen contamination. From these results, it appears that
oxygen enters the sample only in combination with hydrogen. Therefore, in order
to minimize the oxygen contamination, the hydridation time must be decreased,
which also has the effect of decreasing the hydrogen content of the TiH films. The
and 15 - 35 psig followed by a 16 hour anneal at 250°C. This process was repeated
using deuterium (instead of hydrogen) at a pressure of 16 psig. Eight titanium
deuteride samples were produced in two runs. The samples had a composition of
2.2 Backscattering Analysis of TiD Thin Films
films in order to determine the precise sample composition. A tandem-mode NEC
3SDH (1 MV) Pelletron accelerator was used to produce beams of 2.0 - 3.10 MeV
Hett ions. The scattering geometry was such that the single axis of rotation of the
sample was coplanar with the incident and scattered beam directions and perpen-
dicular to the incident beam direction. A scattering angle of 170° was used. The
backscattered particles were detected using a Si surface barrier detector, which sub-
tended a solid angle of approximately 8 mSr. Signal processing was accomplished
using an Ortec 142 Charge-sensitive preamplifier, an Ortec 572 spectroscopy ampli-
fier (using a 1 us shaping time), a Canberra 8075 100 MHz ADC, and a Canberra
S100 multichannel analyzer (MCA). A detector bias of 50 V was provided through
the preamplifier by an Ortec 428 detector bias supply. The energy resolution of the
detection system was typically 18 keV (FWHM).
mine by backscattering analysis the oxygen concentration in bulk of the titanium
deuteride layer. This is due to the fact that the small oxygen signal is superimposed
over the much larger Si signal of the Si substrate and is lost in the statistical fluc-
tuations. The height of the oxygen signal can be increased by as much as a factor
of 25 over its Rutherford value [3,4] by use of the resonance energy, allowing the
detection of as little as 0.2 at% oxygen in Ti (for the given sample configuration).
Below is a brief explanation of how the oxygen concentration of the sample is deter-
mined by the height of the oxygen signal. The analysis is valid for backscattering
Assuming a composition of Tij;_,-,D,O, (where 0 < x,y, < 1), the height of
ential scattering cross section for oxygen scattering a Hett ion of energy E through
an angle of 170°, € is the energy per channel of the MCA, [e(E)]Z'?° is the stopping
cross section factor for Het* of energy E in Tiy-,-,D,O, assuming it is backscat-
tered by an oxygen atom, and 6,7 is the tilt angle of the sample normal in relation
to the incident beam direction.
(using a BIC 1000 Current Integrator); however, there is an uncertainty of about
10% due to secondary electrons and neutral beam effects. The detector solid angle,
Q, also has a significant uncertainty due to the difficulty in measuring it precisely.
Therefore, the quantity QQ was obtained using the height (H 3 ©?) of the Si signal
from the SiO, layer as a reference. This method is quite reliable, since there is no
channelling in the amorphous SiQ2 layer, and its composition and stopping power
are well known. Using the Si in 5102 height as a reference, the formula for the
Hrivo _ (3H3°7) oo( Si 92
0 HSE) gC) [e( BBP ee)
where the factor of 3 comes from the fact that Si atoms make up only one third of
the atoms in SiOz.
The stopping cross section factor, [e(£)|, is a description of the energy loss of
the He ion along both its inward and outward paths in the material. For the general
[e(E)]4? = sec Or (KxeAn Bm (E) + sec Ope4~Pm(KxE)), (2.3)
is the stopping cross section (in units of eV cm? per atom) of a He ion of energy E
in the material A, Bm, and Kx is the kinematic factor for He scattering at an angle
of 170° from atom X (i.e., a He ion with energy E immediately before striking atom
X will have energy Kx E immediately after striking atom X). X may be either A,
B, or any impurity atom that happens to be in the compound. Using Bragg’s rule,
nBm — me 2.4
° (tas + (ta) G4)
The above analysis can be performed on the stopping cross section factor for
the TiDO layer to explicitly show its dependence on the oxygen concentration, y.
[e(E)]G'P° = KoeT?? + sec OpeT?°(KoE)
= Ko((1—2—y)eT(B) + 2e?(B) + ye°(E))
+ sec Op (a —2—y)eTi(KoE) + 2e?(KoE) + ye°(KoE))
= (1-2 —y)le(E)]O' + 2fe(E) + yle(E)l6, (2.5)
off a solitary oxygen atom in a pure Ti matrix. Substituting this result into equation
Len eENG (eg) |” SHE eolk) HIE™
are easily calculated. For Rutherford scattering, the ratio os:(F)/ao0(E) can be ap-
proximated as Z2;/Z3, (where Z is the atomic number), or the individual scattering
cross section values can be found in tables (such as Table X. of Ref. 5). However,
when the oxygen signal is due to 3.05 MeV resonant scattering, a9(E) becomes
system dependent and is more difficult to calculate.
energy straggling along the incoming and outgoing paths and the detector resolution
can significantly broaden the resonance peak. with the additional effect of reducing
the peak yield value. (The total resonance peak area is conserved for a homogeneous
material.) By using a standard, such as SiOz the effective HWHM and peak oo(E)
value for a given incident beam energy can be determined for the system. SiOz on Si
is an excellent standard because it has a well defined oxygen concentration and the
Si signal is relatively flat in the region of the oxygen signal, making Si background
subtraction easy. The peak oxygen signal height can be compared to the height of
the Si signal in the SiOQ2 layer on the same spectrum to determine the effective peak
osi(Er) 2H3i°? [e(Er) 2°?”
traction of the Si background, H S102 is the Si height corresponding to He ions
with 3.05 MeV immediately before scattering, and the factor of 2 is due to the
fact that there are twice as many oxygen atoms as Si atoms in SiO». The value
of oo(ErR)es¢/osi(ER) determined by the SiO2 standard can then be substituted
into Eq. 2.6 for spectra taken under the same conditions (i.e., same incident beam
energy and detector resolution).
depth of 80 nm in pure Ti. To determine the bulk oxygen concentration in the
film after deuteridation, a beam energy of 3.084 MeV was used, corresponding
to a depth of 80 nm in TiD,.7 (my best guess of the composition, based on the
results from the titanium hydride samples). Spectra of two of the samples (one
from each deuteridation run) and the (Si)/SiO2 standard were taken before and
after the deuteridation process. Comparing the signal heights from the standard, it
was determined that co0(Er)efs/o5i(Er)=4.38+0.05, which is 14.6 times the value
for pure Rutherford scattering. Figure 2.3a shows the spectra for sample Til0
before and after deuteridation. Figure 2.3b shows the oxygen signals with the
Si background subtracted. (The small peak at higher energy is the non-resonant
oxygen signal from the surface TiO2 layer.) The height of Gaussian fits to the
oxygen signals were used to determine the peak oxygen height, since the statistics
of the peak were too poor (for these 20 minute, 88 wC Het* spectra) to allow a
is used with z = 0 since the deuterium concentration is assumed to be zero. For the
two samples analyzed, the oxygen concentration was calculated to be 1.3740.25 at%.
The uncertainty is indicative of the uncertainties involved in subtracting the Si back-
ground, determining the oxygen peak height, and uncertainties in the stopping cross
section factors. Stopping cross section values were calculated using the polynomial
fit coefficients given in Table VI. of Ref. 5, except for that for oxygen, which was
calculated using the “corrected” values for oxygen in solids given in Ref. 7. For
the deuterided samples, the deuterium concentration z is not yet precisely known.
However, y can be plotted as a function of « (Fig. 2.4 for sample Til0 after deu-
Lo tttese SD/Si05/TiD,,
12000
500 1000 1500
after deuteridation, with the 3.05 MeV oxygen resonance occurring at a depth of
80 nm.
wn
vo
1000 1020 1040 1060 1080 1100 1120 1140
fits to oxygen resonance signals (lines) for the spectra shown in Fig. 2.3a.
0 10 20 30 40 90 60 70 80 90 100
tration for sample Til0 based on the peak height of the oxygen resonance signal
and Eq. 2.6. The two dashed lines delineate the range of uncertainty in y.
2.2.2 Determination of Deuterium Concentration
is less than that of He, and only atoms with mass greater than that of He will
backscatter He. However, the presence of a sufficient quantity of deuterium in the
Ti film can produce measurable changes in the Ti signal from that of pure Ti. The
presence of deuterium decreases the Ti signal height and increases its width. The
increase in width is caused by the additional electronic energy loss on both incoming
and outgoing paths due to the deuterium. The height of the Ti signal is proportional
to the areal density of Ti atoms encountered by the incident beam per unit energy
loss. Any impurity atom which contributes to the energy loss will decrease the Ti
signal height in proportion to the amount of energy loss it produces. Therefore,
if the change in the Ti signal height is to be used to determine the deuterium
concentration, the effects of all other impurity atoms in the sample must be taken
into account.
oxygen. Assuming the Ti film had the composition Tij_,O, before deuteridation
HAIPO = (1 — yori(E)QQ [e(E)|ziP° cos Or (2.84)
i E
HF! = (1 — z)ori(E)QQ [s(E EO cosy (2.8b)
BRO Tae [etENROO
and assuming z, and therefore [e(E)|##°, is known, the relationship between x and
anf.) HE RCE
(2.10)
independent of Eq. 2.6; therefore, these two curves should intersect. The intersection
point on the z-y plane indicates the deuterium and oxygen concentration of the
sample.
samples that were used to determine the oxygen content. Spectra were taken before
and after the deuteridation process. All four spectra had the same energy calibration
and the target tilt angle was 20° for all samples. The height of the Si signal from
the SiQg2 layer of the substrate was used as a reference to insure that all spectra had
_ the same integrated charge. A comparison of the spectra for sample Til0 before and
after deuteridation is shown in figure 2.5. The ratio HZ!?° /H#?° was determined
to be 0.831+0.004 for both samples.
z=1.37 (the value determined in the oxygen resonance analysis) and Eq. 2.6 (also
for sample Til0). The two curves intersect at c=62.84+2.3 at%, y=1.140.1 at%. The
intersection point for the second sample is almost identical. Therefore, backscat-
tering analysis shows the composition of the titanium deuteride samples to be
25000 L —
sree
20000 + 4
w ' S; 1
2 15000 - 5
3 ; ;
10000 F 4
5000 F : a
Py | ! { \ | NG _/ ; i , |
deuteridation. Ti signal height decreases and width increases due to the energy
absorption of deuterium.
2.0 ‘
] T
(0 signal)
Deuterium Content x (atZ%)
deuterium concentrations for sample Til0. The intersection point indicates a com-
position of Tig.36Do.6300.01. The dashed lines delineate the range of uncertainty for
each equation.
2.3 X-Ray Diffraction Analysis of TiH Thin Films
tion. The sample was hydrided with the exact procedure used for the titanium
deuteride samples, except that hydrogen instead of deuterium was used. Backscat-
tering analysis of the titanium hydride sample showed it to have a concentration
nearly identical to that of the deuteride samples (i.e., TiHj.7).
better comparison could be made to existing X-ray data. As can be seen on the
Ti-H phase diagram (Fig. 2.7 [1]), the composition determined by backscattering
analysis is within 1 at% H of the border between the fec 6 phase and the fet ¢ phase.
From Ref. 1, at room temperature, the lattice parameter (ag) increases linearly
from 4.40 Afor 60 at% H (the (a+6)/6 boundary) to 4.44 Afor 64 at% H (the 6/e
boundary). For the ¢ phase, a=4.51 Aand c=4.37 Aat room temperature for 65 at%
H.
sitive detector [8]. The incident beam direction was 80° from the sample normal.
Spectra were taken of the titanium hydride and an unhydrided Ti sample (Fig. 2.8).
In the pure Ti spectrum, the <002> and <103> peaks of the pure Ti are seen, and
indicate lattice spacings 0.5% larger than the tabulated values [1]. In the tita-
nium hydride spectrum, there is one large peak, which is most likely the <111>
peak, and three small peaks, which most likely correspond to <200>, <220>, and
<311> reflections. The average lattice parameter calculated for the four peaks is
4,.53040.01 A. This is 2% larger than that expected for the fcc 6 phase, and 0.4%
larger than the a spacing for the fct € phase [9]. The peaks appear to be more
consistent with the 6 than the e phase. The larger than expected lattice parameter
gs
is
rd
Ti Atomic Percent Hydrogen
the fct € phase.
two theta
two theta
are consistent with an fcc structure with a lattice parameter of 4.530 A.
Layer Analysis, Vol. 1, O. Meyer, G. Linker, and F. Kappeler, eds., (Plenum
Press, New York, 1976) p. 303.
demic Press, New York, 1978).
Instrum. Methods B 34, 459 (1988).
Chapter 3
with a beam of heavy ions (Xe and Ar) with energies of a few hundred keV and
to detect any fusion products (p, T, ?He*t, or n) of the D-D fusion reaction. By
determining the number of fusion events per incident ion and the distribution of
energies of the fusion products, information about the nature of the processes occur-
ring during ion irradiation of titanium deuteride can be inferred. A silicon surface
barrier detector was used to detect the protons, tritons, and ?He. (It could not de-
tect the neutrons since it detects only charged particles.) A neutron detector could
have been used as well, but it would have been placed outside the target chamber,
at a considerable distance from the sample. Also, the background neutron count
rate (with no beam) was quite large (10-40 counts/minute) and highly variable.
ode source was used for the ion irradiation (Fig. 3.1). The ions are fully accelerated
before mass analysis by a 30° analyzing magnet. Quadrupole lenses before and
after the magnet provide beam focusing. After the second quadrupole lens, a 6°
bend in the beamline removes neutral atoms. A two-stage x-y beam scanner raster
scans the beam through a set of vertical and horizontal beam-defining slits onto the
28ers jy1 ] A
uerg feo1qJ8A uwinjod
aeIS yl \ dung moreno (22¥
wees feqdozO}] a3 eonzeA — wOIsNytqd
a82IS pud mw 2 BATRA,
UBIC [BI119A 9 SHS aD
OP feta,
URI [B1U071I0}] poa\
dain O41 LLL A /
dung Woy
sample using a BIC 1000C current integrator. The target chamber is pumped with
a CTI-7 cryopump and liquid nitrogen cold shroud to a pressure of 1 x 1077 Torr. .
The target holder contains a central cavity that can be filled with liquid nitrogen
used for detection of the fusion products. An Ortec 428 detector bias supply was
used to provide a +50 V detector bias. Signal processing was accomplished using
an Ortec 124A charge-sensitive preamplifier. an Ortec 572 spectroscopy amplifier
(using a 1 us shaping time), a Canberra 8075 100 MHz ADC, anda Canberra $100
target chamber of the Pelletron 1 MV ion accelerator in a 170° backscattering
configuration. Alpha particles of 2.814, 2.614, 2.328, and 1.725 MeV obtained by
backscattering 3.05 MeV He** ions from Au. Rh, Co, and Si samples, respectively,
were used for the calibration. The incident beam energy was determined to within
~2 keV by maximizing the 3.05 MeV !®O(a,a)!*O resonance signal from a ~6.5 nm
surface SiO layer on Si. The system energy resolution (FWHM) was determined
to be 21.9 keV by measuring the 12%-88% width of the high energy edge of the
backscattering spectrum of a thick (200 nm) gold layer. For the electronics chain
settings used throughout the experiment, the energy calibration was determined to
Samples were mounted on 0.125” thick aluminum plates using silicone heat conduct-
ing paste. The plates were bolted onto the hexagonal target holder, which could
sample normal tilted horizontally 7° from the beamline axis. The beam-defining
slits were adjusted to irradiate a 1 x 1 cm region of the sample centered around the
beamline axis. The detector was mounted on an assembly fixed to the top of the
target chamber, i.e., it did not rotate along with the target holder. Two slightly
different detector positions were used over the course of the experiment. In the
first position, the center of the detector was 2.38+0.03 cm from the center of the
sample, at an angle of 51° above the sample normal resulting in a 128.6° angle from
the incident beam direction. In the second position, the center of the detector was
2.22+0.03 cm from the center of the sample. at an angle of 50° above the sample
conversion from particles detected to particles emitted (assuming isotropic distri-
bution) is inversely proportional to detector solid angle. Since the particles were
not emitted from a point source, but over an area of 1 cm’, the effective solid angle
is the average of the solid angles over every point within the area emitting parti-
cles. For simplicity, it was assumed that the ion beam current was uniform over
the entire sample area, so that no weighting was involved in the averaging process.
The calculation was done by computer, with a grid size decreasing until no signif-
icant change in the solid angle resulted (1/80th cm x 1/80th cm). The calculated
effective detector solid angle was 50.8+1.1 mSr for the first detector position and
backscattered and sputtered ions from reaching the detector. If these particles were
allowed to reach the detector, they would cause a low energy background signal
minimally distorts the spectrum of the fusion products while stopping the maximum
possible fraction of “undesired” particles (i.e., the thinnest filter able to stop all .
the “undesired” particles). The most penetrating of these particles is a sputtered
deuteron. The maximum possible energy of a scattered deuteron is a function of
the irradiating ion mass and energy. Of the irradiations studied in this experiment,
600 keV Ar*+* produced the highest energy deuterons (109 keV). Considering that
a deuteron can be reflected at any angle by a Ti atom and retain at least 85% of its
was a 1.35 mg/cm? (5 wm) aluminum foil, which was far thicker than necessary
to stop all undesired particles, but was readily available. In fact, it was so thick
that it stopped the *He ions as well. However, the spectra obtained with this
filter were absolutely assured of being free of background due to the sputtered and
designed to be optimally thin for 600 keV Ar** irradiation. The process by which
this filter was made is described in Appendix 1. The composition and thickness
of the SisN, filter were determined by 2 MeV Het* backscattering analysis to
be Si3N3.32 and 5.57 x 10'® atoms/cm? (190 yg/cm?), respectively. Assuming a
value of 3.44 g/cm?® [1] for the specific gravity, this translates into a thickness
of 540 nm. This thickness is thinner than that calculated necessary to stop all
sputtered deuterons, but the fraction of sputtered deuterons with enough energy
(~60 keV) to get through the filter is so small that their effect on the spectrum
should be negligible. Moreover, the maximum energy of a deuteron after passing
the setting of the lower level discriminator on the ADC). Since this filter was not
optically opaque, all viewports in the target chamber were closed to prevent light
from reaching the detector, and it was visually verified that no target luminescence
and the other with the thin SisN, filter. The titanium deuteride samples were
irradiated with 140, 250, 400, and 500 keV Ar, and 250 keV Xe while using the
Al filter; and 150, 300, 450, and 600 keV Ar. and 200, 300, and 500 keV Xe while
using the Si3N, filter. Ion doses ranged from 1.5 x 101° to 5.2 x 10!" ions/cm? for
irradiation durations of 1 to 7.5 hours. Beam currents ranged from 0.4 to 12.0 vA
for the 1 cm? area irradiated. During irradiation, the samples were kept at liquid
nitrogen temperature to minimize any radiation-enhanced diffusion or desorption
of deuterium from the sample surface. The accuracy of the current integration was
checked by implanting the beam into a piece of Si immediately before and after the
two pieces of (111) Si of similar size. The target chamber was pumped down to
the base pressure of 1 x 107’ Torr, and the target holder (containing all three
samples) was cooled to liquid nitrogen temperature (~ —180°C). A beam of the
desired ion and energy was obtained, maximized, and checked for stability. Once a
stable beam was achieved, the first Si calibration sample was irradiated to a dose
where the fusion products were expected to appear. During the first 10 minutes
of irradiation, these windows were modified (if necessary) to minimize background
counts within the windows while insuring that all legitimate fusion products were
within the window boundaries. Once the irradiation started, the integrated charge
and counts within the proton, triton, and (for the Si3N, filter) >He windows, were
recorded at five minute intervals for the duration of the experiment. Also, the fusion
spectrum was saved at 30 minute intervals so that comparisons of peak shapes over
the course of the experiment could be made. The irradiation was continued until
' sufficient statistics were collected to accurately determine the fusion yield or until
the fusion yield dropped significantly (indicating that most of the titanium deuteride
second $i calibration sample was moved into place and irradiated to a dose of
1 x 1016 ions/cm? under the same beam conditions as the titanium deuteride sam-
ple. The target holder was warmed up to room temperature, and the samples were
removed. When all samples for the given run (Al filter or SisN4 filter) had been
completed, all samples (titanium deuteride and Si calibration) were analyzed by
2 MeV and 3 MeV backscattering spectrometry. The RBS measurement of the ion
dose in the Si samples was used to correct the ion dose determined by the integrated
below lists the irradiations performed for each sample (in the order that they oc-
curred), ion dose for each irradiation, and filter used. For samples which were
irradiated more than once, the higher energy. lower dose irradiation was performed
(keV) (ions/cm?) (hours)
Ti4 Xe 250 5.20 x 1017 7.0 Al
Tid Ar 250 3.78 x 1017 4.0 Al
Ti6 Ar 500 5.20 x 107° 5.5 Al
Ar 400 6.26 x 107° 5.5 Al
Ti7 Ar 140 5.20 x 101” 6.0 Al
Ti9 Ar 600 1.95 x 10'6 2.0 SisN,
Ar 450 2.45 x 101° 2.0 SisN4
Ar 300 2.69 x 101” 1.0 Sis Ny
Ar 150 3.05 x 1027 2.0 Si3N4
Ti10 Xe 200 4.47 x 1017 7.5 Si3Ny
Till Xe 500 153x100! 3.0 Si3N4
Xe 300 2.09 x 1017 3.0 SizN4
The first type of measurement was to take a spectrum without ion irradiation for
a duration of 7 to 40 hours. (A typical spectrum is shown in Fig. 3.3a.) This
background measurement indicates the background due to detection-system noise.
There was no discernable difference between the “no-beam” spectra taken with and
without the titanium deuteride sample present. The number of background counts
increased linearly with acquire duration, with a count rate of 1743 counts per hour.
Almost all counts had an energy of less than 700 keV, and no background count
was ever detected with an energy greater than 2 MeV.
of titanium hydride (not deuteride) with 250 keV Xe+. No nuclear reactions are
expected from this irradiation. One irradiation of 6.0 x 10'® ions/cm? over a dura-
tion of 75 minutes was performed (Fig. 3.3b). There was no significant difference
between this spectrum and a spectrum taken for a similar duration with no beam.
0 S00 861000 1500 2000 2500 3000 3500
a duration of 14 hours. Background count rate = 18 counts/hour.
2h 4
cL J
a]
[e)
Te 4
0) LH | sob tt tl on
0 900 1000 1500 2000 2500 3000 3500
Figure 3.3b Background spectrum taken citing 250 keV Xe* irradiation of TiH, 7.
rate = 15 counts/hour.
roughly equal areas corresponding to 3.02 MeV protons and 1.01 MeV tritons from
the D(d,p)T nuclear reaction. The energies of the detected protons and tritons are
reduced from these values by a few hundred keV due to the energy lost in the Al
filter and due to a Doppler shift (since the center of mass velocity of the deuterons
usually contains a component into the sample and thus away from the detector).
The 0.82 MeV *He ions produced by the D(d,n)*He reaction did not have enough
energy to penetrate the Al filter, and so were not detected. The spectrum obtained
by irradiating TiD, 7 with 400 keV Art* ions to a dose of 5.12 x 101° ions is shown
in figure 3.4. It can be seen that the low energy edge of the triton peak is cut
off. This is due to the lower level discriminator (of the ADC), which was set to
cut off the majority of the background counts caused by noise in the detector and
preamplifier.
that scaled linearly with the counts in the proton peak. This background was not
present in the spectrum obtained by irradiation of the titanium hydride sample, and
is, therefore, due to the fusion events. The most likely source of this background is
protons created by the fusion reaction that were either scattered before entering the
detector or entered the detector through a varying amount of epoxy surrounding
the central area of the detector. Since these particles were not originally emitted
toward the direction of the detector solid angle, this background was not included
in the number of protons detected that was used to calculate the fusion yield.
Oo}
@)
TTT TTT TY TTT TTT TT tt yr rt
—_—_——
Energy (keV)
ions over a duration of 5.5 hours. A 5 ym Al filter was placed in front of the detector
to block sputtered and backscattered particles. The detector was placed at an angle
of 129° from the incident beam direction and subtended a solid angle of 44.1 mSr.
400 keV Art+ irradiation. Proton and triton counts are plotted versus ion dose
instead of time because it is the ratio of proton counts to incident ions (not time)
that is used to determine the fusion yield. Also plotted are the computed time
derivative of the ion dose (instantaneous ion current), and the derivative of the
proton and triton counts with respect to ion dose (instantaneous detected fusion
yield). These plots were used to determine if any significant change in the fusion
yield occurred over the course of the irradiation (which would indicate a change in
ton and triton counts per incident ion over the course of the irradiation. These two
irradiations were 250 keV Xet and 140 keV Art, which had the highest sputtering
coefficients and shortest projected ranges of the five irradiations. Both displayed a
drop in fusion yield at the beginning of the irradiation, a leveling off, and a drop
to nearly zero at the end of the irradiation. The drop at the end of the experiment
could be definitely related to the near complete removal of the titanium deuteride
layer by sputtering. It is conjectured that the initial drop in the fusion yield was
due to the dilution of the deuterium concentration by the addition of the irradiating
species, and that the leveling off occurred when a steady-state concentration profile
was achieved. No significant drop in fusion vield occurred in the other three irra-
diations because the samples were not irradiated to the point where the deuterium
concentration was significantly diluted. Enough statistics were obtained to calcu-
late the fusion yield before this point was reached. A second possibility is that ion
irradiation caused the desorption of deuterium in the cases where the fusion yield
decreased; however, current models of heavy-ion-induced desorption of deuterium
I 8.0 pe pee
5.0 E j
x 9 256 q
€ bd E 7
24.0 ‘ [ q
c c2.0F 4
2 2 a |
© 3.0 x E 1
ve) O15st 4
= ~ ft J
vo r 4
® 20 2 ef J
3 gor 4
a o J
51.0 Bost 4
Oo 9p mr Oo Or
Time (min) Time (min)
Proton Counts (Proton) Detected Fusion Yield
10000 TT a 2.5 -— T rr TF
| | e o£ 1
BO00 + 4 22.0 PNK 7
o rE 4 m 5 4
3) 7 [ q
& 6000} 4 O1oe 4
> aa 4
a | | = fF :
g o,f ;
S 4000+ + = 1.0F :
5 L
2000 + 4 Sost 4
a m 4
L 4 Q L 4
fe) : t : a Ll 1 1 \ r oUt 41 A J . joo. 1 4
Triton Counts (Triton) Detected Fusion Yield
8.0
8000 f- 4 2 2.0F 5
~o ad L 4
2 L 4 o IRON ON 1
rs) T } 4
2® 6000+ 4 01.5; 4
o a r 4
fas} | | L 4
é 3. fF 1
& 4000+ 4 = 1.0F 4
= t 4
iE | : Bf 1
2000 + 4 205b 4
a r 4
r 4 a i a
fe) Fn re SO es ne a gob 1. a
Art? irradiation of TiD, 7.
Yaer 4
Y= det #7
Leorr Quaet
detected per incident ion), Icorr is the correction to the ion dose as determined
by backscattering analysis of the Si calibration samples, and Q4g.; is the detector
solid angle (44.1 mSr for these irradiations). The formula assumes that the angular
distribution of reaction products is isotropic. This assumption is reasonable for
deuteron energies <~30 keV (Lab frame) [4]. The ion dose in the Si calibration
samples was measured using 3 MeV Het+ backscattering analysis. A target tilt
angle of 7° was used to avoid channeling. The ion dose measured by backscattering
analysis was 5+3 percent greater than that measured by charge integration for all
Si calibration samples. Therefore, a value of I-9rr=1.05 was used in Eq. 3.1 for all
irradiations.
sidered. Using the triton peak could not have yielded as accurate a result as using
the proton peak because the triton peak was partially cut off and the region of the
triton peak also contained background from both deflected protons and detection-
system noise. For the cases where the detected fusion yield remained fairly constant
throughout the irradiation, the precise value of Yy.; was determined by the slope
of the least-squares fitted line to the number of protons detected as a function of
the number of incident ions. For the cases where the fusion yield dropped over
the course of the irradiation, only the portion of the irradiation before the drop in
detected fusion yield was used in the least-squares fitting procedure. The fusion
yields calculated using Eq. 3.1, along with experimental parameters, are shown in
Al filter, determined using Eq. 3.1. Ion dose and proton counts are listed to show
the statistics available for the calculation.
(keV) (ions/cm?) (fusion events/ion)
Xe 250 4.04 x 107° 69 (4.82+0.72) x 107}%
Ar 140 1.38 x 107” 570 (1.3540.14) x 107!”
Ar 250 3.78 x 10!" 16643 (1.2940.13) x 107!
Ar 400 6.26 x 1016 9827 (5.32+0.54) x 107"
Ar 500 5.20 x 1016 23712 (1.0340.10) x 107!°
using the Al filter in that the *He ions were also detected and that the reduction of
the peak energies was smaller due to the smaller energy loss in travelling through
the SisN4 filter. Even though the energy loss and energy straggling in traversing
the SiN, filter was only ~15% of that for the Al filter, the proton and triton
peak shapes (FWHM) were quite similar to those obtained with the Al filter for
irradiations of the same ion and similar energy.
of all spectra obtained using the SigN, filter) is shown in figure 3.6. The region
between the proton and triton windows contains a uniform background similar to
that obtained with the Al filter. Figure 3.7 contains plots of the recorded values of
the ion dose, and proton, triton, and *He counts, and their respective derivatives
over the course of the 500 keV Xe** irradiation.
90
70
60
30
40}
30
20
tO ~
0 000 1000 1500 2000 2500 3000 3500
Loo
Xett ions over a duration of 3 hours. A 540 nm Si3N, filter was placed in front
of the detector to block sputtered and backscattered particles. The filter was thin
enough to allow the 0.82 MeV *He to reach the detector. The detector was placed
at an angle of 130° from the incident beam direction and subtended a solid angle
150F s Ud ]
Ot 7 o 5 4
Sf S15 4
Pr [ ] eter 1
fe} L 4
21.00 4 ow L 4
o L d nN i 1
‘oO I 2 1Or 7
= [ ® q
a 0.50} 4 Sct j
a ' ' = 05 f 4
c J w L 4
2 [ 1 s r ; |
phi ran Serre fo
(o) 50 100 150 [9] 50 100 150
Time (min) Time (min)
1500 —r—+_roton Counts 1.20 + enoton) Detected Fusion Yield __
L i € , d
[ N1.00F 4
me] r 7 a
2 r 1 a r 1
8 1000h 4 7 0.80} 4
- q 4 9 L. 4
6 [ 1 ~~ 0.60 + 4
> 500+ 4 > 040+ 4
[a 5 4 o L 4
a j 2
f 1 20.20} 4
ok SO ple 1, a st
0 0.50 1.00 1.50 0 0.50 1.00 1.50
lon Dose (10'® ions/cm?) lon Dose (10'® ions/cm?)
Tri Tri i i
1500 riton Counts a 1.20 ¢ riton) Detected Fusion Yield —
~ 1.00F 4
Be] r 7 Lal [ J
Brod r 1 on
— F 4 o L. 4
8 f ] 9 0.60 + 7
= 500+ 4 7 040+ 4
& L ; ° . ;
[ i 8 0.20b 4
oe 9 pba su i pod
fe) 9.50 1.00 1.50 0 0.50 1.00 1.50
lon Dose (10'§ ions/cm?) lon Dose (10!'8 ions/cm?)
i t i t Fusi Ytel
T T a 1 T T
r 1 3g 100F ALY |
® L | x L i
9 1000 4 = o.80b 4
=_ J ron] L J
i —
Oo r ] “060+ 7
2 500 t 4 * 0.40F 4
z ; 3 + ;
r 1 6020+ 7
r 1 2
- 4 ry , 4
re) Fa DO PO | O ghee tia po sit
0 0.50 1.00 1.50 (e] 0.50 1.00 1.50
Ion Dose (10!'8 ions/cm?) lon Dose (10'§ ions/cm?)
500 keV Xet* irradiation of TiD, 7.
irradiation also decreased, since both the 250 and 300 keV Xe? irradiations did,
but the poor proton count statistics made this difficult to determine.
was considered. Although the triton and *He peaks were not cut off (except for
3He for 600 keV Art*), the regions of those peaks still contained background from
both deflected protons and detection-system noise. Just as for the Al filter, when
the detected fusion yield remained fairly constant throughout the irradiation, the
precise value of Y;., was determined by the slope of the least-squares fitted line to
the plot of the number of protons detected as a function of the number of incident
ions; and when the fusion yield dropped over the course of the irradiation, only the
portion of the irradiation before the drop in detected fusion yield was used in the
least-squares fitting procedure. The correction to the ion dose (Icorr) varied from
1.02 (for all Ar irradiations) to 1.14-1.26 (for the Xe irradiations). The fusion yields
calculated using Eq. 3.1 are listed in Table 3.3, and plotted, along with the fusion
SigsN, filter, determined using Eq. 3.1. Ion dose and proton counts are listed to
show the statistics available for the calculation.
(keV) — (ions/cm?) (fusion events/ion)
Xe 200 4.47 x 10"" 174 (8.3 +1.7 ) x 1074
Xe 300 3.70 x 101° 219 (1.24+0.18) x 107?”
Xe 500 1.53 x 1078 1381 (1.80+0.18) x 10711
Ar 150 1.84 x 101” 1315 (1.7340.17) x 1071?
Ar 300 2.69 x 10!” 32291 (2.960.30) x 10713
Ar 450 2.45 x 101° 7943 (7.94+0.80) x 1071?
c C
an Al filter (©) or a Si3Nq filter (A) in front of the detector.
Florida, 1978) p. B-161.
Appl. Phys. A 42, 19 (1987).
Appl. Phys. A 42, 179 (1987).
150 (1987).
Chapter 4
the experimental fusion yield must be compared to predictions based on the different
processes suspected of causing the fusion events. At the outset of the experiment,
two possible mechanisms for producing fusion events were considered: high energy
deuteron recoils in the early stages of the collision cascade and, although unlikely,
“cold fusion” processes in the thermal spike regime at the end of the cascade. As
no models of the “cold fusion” processes or values of “cold fusion” cross sections
are available, no realistic predictions of fusion yields for “cold fusion” processes can
be made. On the other hand, the early stages of the collision cascade caused by an
energetic ion (>1 keV) are believed to be well understood (see Section 1.2). Well es-
tablished models exist [1,2], and are regularly used to predict implanted ion profiles
(projected range and straggling), sputtering coefficients, and defect concentration
profiles [3,4]. Therefore, the first step is to calculate the fusion yields expected
based on a binary collision cascade model and compare them with the experimen-
tal fusion yields. Only if the experimental yields are significantly higher than those
predicted by the binary collision cascade model would there be any need to consider
additional processes (such as “cold fusion”) to account for the experimental results.
several possible methods that can be used to calculate the fusion yield. Perhaps
the simplest method would be to use a Monte-Carlo simulation. I have already
fusion cross sections. However, the fact that the experimental fusion yields are on
the order of 107'°-1071* fusion events per incident ion makes the task of collecting
sufficient statistics quite daunting. Therefore, a method of calculating the fusion
yields analytically is preferable.
yield is expressed as a finite sum of integrals, which can be solved numerically. The
first method begins with the D-D reaction and works backwards through the colli-
sion cascade until the incident ion is reached. The second begins with the incident
ion and follows the collisions until a D-D reaction occurs. Both give identical values
for the fusion yield for a given irradiation and take about the same time to compute
(~2 hours on the pVAX). The first method allows calculation of the fusion yields
for all incident ion energies up to the desired value in a single run, while the sec-
ond method gives the fusion yield for only one incident energy per run. However,
the second method can be used to obtain information about the distributions of
energies for each type of atom in the sample for every generation in the collision
cascade. In this chapter, the first method will be discussed. The second method
target atoms and electrons in nuclear and electronic collisions until it comes to rest.
The first generation recoils (those atoms struck by the incident ion) undergo a sim-
ilar energy loss in transferring their energy to the second generation recoils, and so
transfer of energy to the atom to be labelled. Therefore, for Xe ion irradiation of
titanium deuteride, all first generation recoils are labelled either Xe-Ti or Xe-D, »
no matter how many collisions the Xe ion had undergone before striking the la-
belled atom. Second generation recoils are labelled Xe-D-D, Xe-D-Ti, Xe-Ti-D, or
Xe-Ti-Ti. Third and higher generation recoils are labelled similarly. The label can
be thought of as either a label of the atom or a label of the chain of collisions that
directly led to the transfer of energy to the atom. Each chain label is general in
that it does not specifically state the amount of energy transferred in each collision;
it represents all possible energy transfers for that series of collisions. Therefore, a
generalized collision cascade which encompasses all possible collision cascades for
the given ion and target combination can be described as a set of these chains.
For a fusion event to occur, energy must be transferred to a deuteron, which
in the course of its displacement must strike a second deuteron and cause a fu-
sion reaction. Therefore, each collision chain resulting in a fusion reaction must
begin with the incident ion and end with a deuteron striking another deuteron. For
Xe irradiation of titanium deuteride, the simplest chain leading to fusion is Ke-D—D.
More complicated chains include Xe-Ti-D-D, Xe-D-D-D, Xe-Ti-Ti-D-D,
Xe-D-Ti-D-D, and so on, where the final D-D indicates the fusion reaction. If
the fusion yield for each chain can be found, the total fusion yield due to the inci-
The chains are listed in order of simplicity, starting with the chain involving the
fewest generations (or intermediate collisions).
between unlike atoms can transfer only a fraction of the original atom’s energy to
the next atom, and in collisions between like atoms, the likelihood of a 100% energy
transfer is quite small. Therefore, as the number of intermediate collisions increases,
the energy transferred to the penultimate deuteron becomes smaller and smaller.
Since the D(d,p)T fusion cross section decreases extremely rapidly with decreasing
energy (for the range of deuteron energies produced in this experiment), increasing
the number of intermediate collisions in a chain will decrease the fusion yield of the
chain. There is one special case (which will be explained later) where adding one
Yxexpp is negligible, all chains of the type Yyess:pp or Yxepypp will also have
negligible contributions to the total fusion yield. Therefore, only a finite number
of chains need to be computed in order to establish that the contributions from all
reaction at the end of the chain and works backwards through the chain to the
incident ion. For example, for the chain Xe-Ti-Ti-D-D, the fusion yield Ypp(£p)
for the chain segment D-D is calculated as a function of the initial energy of the
penultimate deuteron, Ep, after being struck by the last Ti atom. Next, the fusion
initial energy of the Ti atom. This process is continued until the yield for the entire
chain, YxeT:iTipp (Exe), has been calculated.
np dE
Ypp(£p) I npo s(Ecm )dz | ep(B) 7! /2) , (4.3)
tively, the atomic densities of deuterons and titanium atoms in the target, ep is
the sum of the nuclear and electronic stopping power of D in TiD,7, and af is the
fusion cross section for the center of mass energy Ecy = Ejq,/2 for the reaction
D(d,p)T. (Note that np/(np +n) is the atomic fraction of deuterons in TiD, 7,
which can be labelled np). This integral is simply the integral of the number of
deuterons the incident deuteron encounters times the fusion cross section for the
energy at which the incident deuteron encounters each deuteron in its path. The
first integral is in physical space, the second is in energy space. It is easier to work
in terms of energy rather than depth because the fusion cross section is a function
of energy and the natural limits of integration are from the initial energy Ep to the
point where no further interactions occur (i.e., E=0).
is calculated by determining the energy distribution of energetic deuterons produced
by Ti—-D collisions, and summing the fusion yield for each of the energetic deuterons.
The number of deuterons per unit energy with energy U created by the Ti atom
vp(U) = np | dU en(B)’ (4.4)
yield for this distribution of energetic deuterons created by the Ti atom of energy
Yqipp (Er) = wm | vp(U)¥pp(U)dU
= NY —~_— dU
| en(E) Jp pp(Up) WU D;
transferrable from a Ti atom of energy Ey; to a deuteron. The second equation is
obtained by substituting Eq. 4.4 for yp(U) and reversing the order of integration.
The integral in Eq. 4.5 sums all possible Ti--D collisions during the slowing down
of the Ti, weighted by the differential cross section.
segment, Ypp. This is true for any size chain segment, and Eq. 4.5 can be generalized
dE, Ya,b%o do(E,,U
¥i..op(Us) 29 any ,
the target, and do/dUp is the differential scattering cross section for a—b collisions.
the yield for the chain segment Ti-Ti-D-D is calculated using Eq. 4.6 with a=Ti,
b=Ti, Ys...pp=Ytipp and Yay... pp=Yritipp. Finally, the incident ion is added to
the front of the chain, and the fusion yield for the entire chain, Yxetitipp (Exe), is
found using Eq. 4.6 with a=Xe, b=Ti, and Y;...95p=Yritipp. The fusion yields for
4.4 Algorithms Used to Compute Fusion Yields
tions must be known: the fusion cross section for the D(d,p)T reaction as a function
of the center-of-mass energy of the fusing deuterons (0 ;(Ecm)); the differential scat-
tering cross section for all possible a—b collisions as a function of incident energy, E,,
and energy transferred, U; (do(E,,U,)/dUs). where a,b=Ti, D, and Xe or Ar (the
irradiating ion); and the stopping cross section in TiDj.7 as a function of energy
(€a(£)) for all a.
fit to the astrophysical S factor determined experimentally in [6]. The differential
—_ _—_— t — ae .
WU 50 FG [1 + (2At*~™)$] , > BU (4.8)
transferable between the two atoms in the collision, c, is the conversion factor
from energy to the dimensionless “reduced” energy [2], and \, m, and q are fitting
parameters dependent on the type of interatomic potential assumed. The values
of A, m, and q for six commonly used potentials are given in Ref. 8. The nuclear
and electronic stopping powers are calculated using the formulas in Ref. 7, except
for the electronic stopping power of deuterons, which is calculated from a fit to
experimental data [9].
be solved by numerical integration. This converts the integral to sums. Equation 4.3
= Ypp((n — 1)AE) + oO AE. (4.9)
=Yi»..pp((n-1)AE) +
do(nAE,jAU)| AUAE
m |% _pp(jAv) ai E(nAB) ° (4.10)
avoid roundoff error in the calculation. Similarly, AE is chosen so that AE=E/n,
where E is the initial energy and n is an integer. Typically, calculations were made
using n=1000 (AE <600 eV), and m; varying so that AU ~500 eV.
incident energy Exe, one begins by calculating the fusion yield Ypp as a function of
energy for the chain segment D-D. Using Ypp, one next calculates Yppp, Yripp,
and Yxepp, the first two being chain segments and the last one being a complete
chain (since it includes the incident ion). Xe-D-D is the first-generation-recoil
fusion chain, since the penultimate deuteron is a first-generation recoil.
above, and the fusion yields for those chains are calculated, giving Ypppp, Yrippp;
Y¥xeppp, Yptipp, Yritipp, and Yxetipp. At this point, the fusion yields of the
added to the front of the chain segments of the current generation, and the fusion
yields for those chains are calculated. In general, there are 2"~! n'" generation .
fusion chains, and to calculate the fusion yields for the first n generations of recoils,
one must calculate the fusion yields of 2"+! — 2 chains and chain segments.
generations of recoils is listed in Appendix 2. Fusion yields were calculated for
both Ar and Xe irradiation of 600 keV using each of the six interatomic potentials
given in Ref. 8 (Thomas-Fermi-Sommerfeld, Bohr, Lenz-Jensen, Lindhard {c?=1.8],
Lindhard [c?=3], and Moliére). This gives the fusion yields for Ar and Xe as a
function of energy for all energies up to 600 keV. The fusion yield for each chain
(segment) took approximately 7 minutes to calculate on the wVAX used. Therefore,
the fusion yields of the first three generations of recoils could be computed in about
on interatomic potential for either Ar or Xe irradiation. In both cases, the total
yield at a given energy varies by less than a factor of two over all six potentials. It
was not necessary to calculate past the third generation recoils for either Ar or Xe
irradiation to obtain all significant contributions to the total fusion yield, although
the fusion yields of the fourth generation recoils were calculated to determine how
For an irradiation at a given energy, the fusion yield for Ar is about an order
of magnitude greater than that for Xe. This is because Ar is able to transfer a
larger fraction of its energy (18.3% maximum) to the deuteron than Xe can (5.95%
maximum). This results in higher energy deuterons, which have significantly higher
from 50 to 600 keV come from the Xe-D—D and Xe-Ti-D-D chains, which together
account for approximately 99.8% of the total vield. The Xe-Ti-Ti-D-D chain is the
next most significant, contributing approximately 0.2% of the total. All other chains
combined give less than 0.005%. The magnitude of the fusion yields for each chain
calculated (using the Thomas-Fermi-Sommerfeld interatomic potential) is shown in
figure 4.1a. The relative contribution of each chain to the total fusion yield is shown
in figure 4.1b. The fusion yields for all chains of up to third generation are shown,
except for that of Xe-D-Ti-D-D, which was too small to be calculated even using
double precision variables. The dotted line represents the highest fusion yield from
a fourth generation recoil chain (Yxerititipp ).
of Xe-Ti-D-D is greater than that of Xe-D--D. Also, the yield of Xe-Ti-D-D-D
is greater than that of Xe~-D-D-D for energies less than 105 keV. These are two
examples of the case where adding one intermediate collision in a chain increases
the fusion yield. The addition of the Ti in the chain increases the fusion yield
because its mass is between that of Xe and D, which means that more energy can
10-10 f
1o-12E
1o-13E
19714
10718
10-16 E
10717
10718]
107205
l 1 I |
300 400 500 600
100 200
Xe irradiation of TiD,.7. The dotted line is the highest yield for 4** generation
recoils (YxeTiTiTiD )-
' '
yoy ar
Xe Energy (keV)
chains shown in Fig 4.1a.
have larger fusion cross sections, and therefore, the fusion yield of the chain can
be increased by adding the Ti. However, as the energy of the Xe increases, the
probability of the high-energy-transfer Xe-Ti and Ti-D collisions becomes smaller
and smaller until the increase in deuteron energy is offset by the decrease in the
probability of creating an energetic deuteron. Above this energy, the normal order
the fusion yield of a chain, two conditions must be met. The first is that the
mass of the intermediate atom be between that of the two atoms it collides with,
so that there is an increase in the maximum energy transferred to the deuteron
with the additional collision. The second is that the energy of the incident ion be
low enough so that the increase in the fusion cross section due to the increase in
deuteron energy is high enough to offset the decrease in the probability of creating
an energetic deuteron. Since the fusion cross section increases most rapidly with
increasing energy at low energies, the increase in fusion cross section due to the
intermediate collision is most pronounced at low energies. Also, the decrease in
probability of head-on (high energy transfer) collisions is least pronounced at low
energies. Therefore, if the additional collision does increase the fusion yield, the
transfer the greatest fraction of the incident ion energy to the deuteron through
M when the mass of M is the geometric mean of the masses of D and J, ice.,
mu=(my, X mp)'/?. For the case of Xe irracliation of MD,, the optimum mass of
M for energy transfer is 16 amu (oxygen), with a 2.6 times increase in the energy
contribution. The Ar-Ti-D-D chain accounts for a little under 1% of the to-
tal yield, and all other chains combined contribute less than 0.01%. The mag-
nitude of the fusion yields for each chain calculated (using the Thomas-Fermi-
Sommerfeld interatomic potential) is shown in figure 4.2a. The relative contribution
of each chain to the total fusion yield is shown in figure 4.2b. The fusion yields for
all chains of up to third generation are shown, except for that of Ar~-D-Ti-D-D,
which has a fusion yield of ~3 x 10~?9 at 600 keV. The dotted line represents the
cannot increase the energy transferred from Ar to D, the chains involving Ti have
higher fusion yields than those of the same generation that involve only Ar and
D. This is because the mass of Ti is close to that of Ar and high-fraction energy
transfers are much more likely for Ar-Ti and Ti-Ti collisions than they are for
D-D collisions. For n** generation chains, the highest fusion yield is from the chain
Ar-(Ti)(,-1)-D-D; the second highest from Ar-(Ti)(n—2)-(D)(2)—D, and so on. The
chain with the lowest fusion yield for a given generation is that which alternates
the most times between heavy and light atoms (i.e., Ar-D-Ti-D-Ti- --). This is
because each Ti-D or D-Ti collision cannot involve an energy transfer of more than
Ar Energy (keV)
Ar irradiation of TiD;.7. The dotted line is the highest yield for Ath generation
recoils (YartititiDp )-
10° E E
O E Ar-O0-D E
of :
~ 10 'E +
C E :
2 c 7
es 1072 I Ar-Ti-D-D ]
— ro-reerun 4
eo) 5 4
_ -3
oO
2 10 E
S q
- 1074 Ar-Ti-Ti-D-O =
° :
5 4
-5 Ar-D-D-D
oO
2 10 =
Ar Energy (keV)
chains shown in Fig 4.2a.
Ar and Xe irradiation. Theoretical fusion yields for four of the six potentials give
an excellent fit to the experimental yields, one gives a marginally good fit, and
the other is noticeably too high. The theoretical fusion yields for Ar irradiation of
TiD,.7 for all six interatomic potentials are compared with the experimental results
for Ar in figure 4.3a. A similar comparison is made for Xe irradiation in figure 4.3b.
The Lindhard [c?=3] potential gives the highest theoretical yield for both Ar and
Xe, which can be seen to be somewhat higher than the experimental yields. All
other potentials appear to be within the scatter of the experimental points. The re-
duced x? for each potential compared to the experimental data is listed in Table 4.1.
The y? values for the two Lindhard potentials are noticeably larger than those for
the other four potentials, which are nearly identical. For the final analysis, I chose
the Thomas-Fermi-Sommerfeld (TFS) potential over the Lenz-Jensen (which had
the same y*) because of its simpler form. Figure 4.4 compares the TFS theoretical
fusion yields with the experimental yields for both Xe and Ar irradiation. The
based on the linear binary collision cascade model. There is no need to consider
additional processes (such as “cold fusion”) to account for the experimental results.
The collision cascade model shows that the fusion events occur mainly in the early
stages of the collision cascade, with the dominant contribution coming from ener-
getic deuterons created within the first three generations of collisions. Thus, the
detection of D-D fusion products in this experiment is a direct observation of nu-
clear collisions occurring in the early stages of the collision cascade produced by
potentials (lines) and experimental fusion yields (data points) for Ar irradiation of
potentials (lines) and experimental fusion yields (data points) for Xe irradiation of
Ar Energy (kev)
Xe Energy (keV)
10 E I ' I , [3
F oo AI filter 7
| oA SigN, filter a4
1979 J
5 L a
© qQ7 L- -
Cc i 4
2 r 7
S101? E
LL E s
rol3L 2
1Q714 I 1 j 1 | f I i | 1 | |
100 200 300 400 500 600
yields for Ar and Xe irradiation of TiD,.7. Theoretical yields were calculated using
the Thomas-Fermi-Sommerfeld interatomic potential, which gives the best fit to the
experimental data.
sections using different interatomic potentials for Xe and Ar irradiation.
Thomas-Fermi-Sommerfeld 2.0 1.2 3.2
Lenz-Jensen 1.9 1.3 3.2
Moliére 2.0 1.5 3.5
Bohr 1.3 2.4 3.7
Lindhard [c?=1.8] 1.1 6.6 7.7
Lindhard [c?=3.0] 7.9 15.4 23.3
the Thomas-Fermi-Sommerfeld interatomic potential for Ar and Xe irradiations of
(keV) (fusion events /ion) (fusion events/ion)
Xe 200 (8.3 41.7 )x 107" 1.03 x 10718
Xe 250 (4.82+0.72) x 1078 4.22 x 10738
Xe 300 (1.24+0.18) x 107}? 1.21 x 107)?
Xe 500 (1.8040.18) x 10722 1.56 x 1071!
Ar 140 (1.3540.14) x 1072? 1.38 x 107}?
Ar 150 (1.7340.17) x 1071" 1.88 x 107}?
Ar 250 (1.290.138) x 107?! 1.40 x 107!
Ar 300 (2.96+0.30) x 107"? 2.56 x 10713
Ar 400 (5.3240.54) x 1077?! 5.95 x 10713
Ar 450 (7.94+0.80) x 1077" 8.12 x 107"?
Ar 500 (1.03+0.10) x 107*° 1.06 x 107?°
Ar 600 (1.92+0.20) x 1071° 1.61 x 10719
in Solids, Vol. 1 (Pergamon, New York, 1985).
and their Applications (Academic, London, 1976), pp. 19-21.
(1990).
150 (1987).
Nuclear Stopping Powers and Energy Straggling for Low Energy Ions (Hahn
-Meitner-Institut, Berlin, 1975), pp. 3-5.
All Elements (Pergamon, New York, 1977).
Chapter 5
widths of the proton, triton, and helium signals varied with irradiating ion and
energy; and that the energy of the peak positions shifted as well. As the same Si3;N,
filter was used for all irradiations, and it was verified by backscattering analysis
that after all irradiations were completed, the filter was virtually unchanged from
its original state, the differences in the peak shapes must be due to differences in
the collision cascades produced by the different irradiations.
ergy loss between the creation of the particle and its detection, and the distribution
of Doppler shifts caused by the distribution of the deuteron—deuteron center-of-mass
velocities relative to the detector. As the peak shapes are the result of a convolution
of many processes (not all of which are precisely known), it would be difficult to
analyze the Doppler shifts by manipulation of the experimental peaks. By modi-
fying the binary collision cascade model discussed in Chapter 4, one can calculate
the distribution of deuteron—deuteron center-of-mass velocities at the time of fusion
and, by assuming an angular distribution of those velocities, compute theoretical
peak shapes for the fusion products and compare with the experimentally obtained
shapes. The analysis procedure is identical for protons, triton, and ?He ions. As
the proton signal is least effected by energy loss between creation and detection,
The first is the Doppler shift due to the motion of the center-of-mass (CM) frame
of the colliding deuterons (from which the particles are emitted) relative to the lab
frame (in which the particles are detected). This shift depends on the magnitude
and direction of the velocity of the CM. The second is the energy loss of the particle
while exiting the titanium deuteride film, which is a function of the depth at which
the fusion event occurred. The third is the energy loss through the Si3N, filter,
which is a function of the angle (relative to the filter normal) at which the particle
penetrates the filter. And the fourth is the detector resolution, which causes the
detected energy of a mono-energetic beam of particles to have a Gaussian spread
with a FWHM of 22 keV.
tanium deuteride is approximately 3.5 eV/Afor 3.02 MeV protons, 15 eV /Afor
1.01 MeV tritons, and 60 eV/Afor *He ions [1]. The maximum depth at which fu-
sion can occur is determined by the range of the incident ion. The largest range in
this experiment is 3000 A(for 600 keV ions) [2], which corresponds to an energy loss
of 11, 45, and 180 keV for protons, tritons, and *He ions, respectively, produced
at that depth. However, most fusion events occur in the high energy region of
the collision cascade, which is significantly closer to the surface than the projected
range of the ion, creating an energy loss distribution on the outward path peaked at
zero and decreasing rapidly with depth. As the maximum energy loss for protons
is 11 keV, the energy loss on the outward path can be ignored for protons.
distribution, the energy loss distribution through the filter is calculated for each
fusion product using a TRIM program similar to that of Ref. [3]. This energy loss
distribution is convoluted with the detector resolution, giving the energy loss dis-
tribution detected for a mono-energetic beam of particles emitted from the sample
surface (Table 5.1). The spectrum for these mono-energetic beams is compared
with the experimental spectrum for 500 keV Xet* irradiation in figure 5.1. The
difference between the two spectra shows the effect of the Doppler shift and (for
tritons and *He ions) the effect of energy loss for fusion events occurring at a depth
in the sample.
detected energy distributions of these particles is found by convoluting those distri-
emitted from the surface.
Particle Energy Loss FWHM FWHM
(keV) (keV) (keV)
proton 18 4.2 22.3
triton 79 10.0 24.1
3He 306 21.6 30.7
layer, it creates a series of collision cascade chains such as J-D and J-Ti-Ti, etc.
—=—_—_- +
tt Ne td dened pont cithy yy
Energy (keV)
500 keV Xett irradiation of TiD;.7. Theoretical yields assume mono-energetic
beams of 3.02 MeV protons, 1.01 MeV tritons, and 0.82 MeV ?He ions emitted
from the sample surface convoluted with the detected energy loss distribution of
Table 5.1. The area under each theoretical signal is equal to the area under the
corresponding experimental signal.
Y7 = Yipp + Yrripp + Yroriripp - (5.1)
wards through the chain to the incident ion. In this method, an iterative equation
for the fusion yield for an ion of energy E based on the yield for energy E — AE
allows the simultaneous calculation of yields for all energies up to E. However, in
calculating the yields in this way, the energy distributions of the atoms involved in
the chain is not accessible.
ion and calculating the energy distribution of first generation D and Ti recoils,
and then, given these distributions, calculating the energy distribution of second
generation recoils, and so on. The fusion yield for a given chain is then calculated by
computing the fusion yield for the energy distribution of the penultimate deuteron
in the chain. (The final deuteron in the chain is at rest.) The fusion yield is
calculated as a function of the incident deuteron energy at the moment of fusion.
The total fusion yield for the incident ion is found by summing the fusion yields
integrated over all deuteron energies for each chain. As an example, the fusion yield
for Xe-Ti-Ti-D—D will be calculated.
VXeTi U)= i u 3 5.2
xen(V) =m [SO (5.2)
atomic fraction of Ti in the target, do(E£,U)/dU is the differential scattering cross
recoils is found by using Eq. 5.2 multiplied by the number of Ti atoms per unit
Vyeniti(U) = nr; / dE, | VxeTi(E;) (5.3)
e...an(U) = dE | e...a( , 5.4
VXe...ab(U) mf a i (£1) dU ea(E) (5.4)
scattering cross section for a—6 collisions, and Ea max iS Yxe-+-+ +: ¥-alxe- Given
VXeTiTi, VXeTITID 18 calculated using Eq. 5.4 with a=Ti, b=D, vxe..a=Vxerit;, and
VXe...ab=YxeTiTip. At this point, the energy distribution of the penultimate deuteron
of the chain has been calculated and can be used to determine the fusion yield of
the chain. A similar procedure is used to calculate the energy distribution of the
penultimate deuteron for all other chains.
deuteron energy E’y,, for the general chain Xe--- D is a function of the number of
these deuterons with energy Ey, or greater, because all these deuterons will lose
energy and eventually have the possibility of causing a fusion event as they pass
through the energy Ey,,. Thus, the number of fusion events per unit energy at
energy Efus is given by
VXe..Dfus(Efus) = 7D (/. ; ro. 0( EME) ree (5.5)
The total fusion yield of the chain Xe--- DD is found by integrating the number
Yxe...DD -| VXe...Dfus(E)dE . (5.6)
incident ion energy because it is simply a rearrangement of the basic terms and a
change in the order of integration from that of Eq. 4.6. The total fusion yields for
each chain are summed (Eq. 5.1) to give the total fusion yield for the given incident
the total fusion yield, the integrals above must be solved by numerical integration,
just as in Chapter 4. A similar conversion from integrals to summations was made,
and simple rearrangements in the order of calculation were made to increase the
efficiency of the computation. The same functions for stopping power, differential
scattering cross section and fusion cross section as those used in Chapter 4, as
well as the same energy increments were used to calculate the fusion yields here.
Because of the large amount of memory needed to store the energy distributions of
each atom in each chain of the collision cascade, the distributions can be calculated
for only one ion energy at a time. Also, because no iterative equation, such as
Eq. 4.10, exists for calculations in the forward direction, there is very little increase
in calculation speed by combining calculations for different ion energies.
500 keV Xe, i.e., the experimental energies used with the Si,;N, filter. Because
the Thomas-Fermi-Sommerfeld interatomic potential was shown (in Chapter 4) to
give the best fit to experimental yields, it was the only potential used in these
calculations. The fusion yields and energy distributions for the J-D-D, J-Ti-D-D,
and IJ-Ti-Ti-D-D chains could be computed in less than 45 minutes on the wVAX.
figure 5.2b. For the case of 600 keV Ar, the number of primary recoil deuterons
is significantly higher than the number of deuterons in all higher generations for
all deuteron energies. Thus, its contribution to the total fusion yield (99.2%) also
dominates. For the case of 200 keV Xe, the number of primary recoil deuterons dom-
inates at low energies. However, the maximum energy for primary recoil deuterons
is 11.9 keV, while the maximum energy transferred to deuterons through the chain
Xe-Ti-D is 24.3 keV (for 200 keV Xe). Above a deuteron energy of 11.9 keV, the
for all cases of Ar irradiation are shown in figure 5.3. The peak energy indicates the
most probable deuteron energy at which fusion occurs, and is a compromise between
high fusion cross section and high differential scattering cross section. These peaks
are analogous to the Gamow peaks for fusion in solar interiors [4]. As the Ar energy
is increased from 150 keV to 600 keV, the energy of the peak fusion yield increases
slightly. However, for 150 keV Ar, the peak energy is 60% of the maximum deuteron
energy, while for 600 keV Ar the peak energy is only 30% of the maximum deuteron
energy. This indicates that as the ion energy is increased, the main contribution to
ations are shown in figure 5.4a. An enlarged view of the fusion yield for 200 keV
Xe irradiation is shown in figure 5.4b, with the contributions of the Xe-D—D and
Xe-Ti-D—-D chains shown with dashed lines. A small high energy tail can be seen for
each of the peaks. This tail is due to the high-energy contribution of the Xe-Ti-D-D
chain. The tail becomes increasingly predominant with decreasing Xe energies due
1o-' fa
1077
10°3
10°45
107°
10°
1077
1078
1079
10710
600 keV Ar
Deuteron Energy (keV)
tion for the three chains giving the largest contribution to the total fusion yield.
Deuteron Energy (keV)
for the three chains giving the largest contribution to the total fusion yield. The
maximum deuteron energy for the Xe-D chain is 11.9 keV.
oF 1
<356 Ar 600 keV 4
c b 4
= 3.0F 2
el EF J
6256 4
> EC J
® a -|
© 206 4
S15 :
xe) ' 7
cab) " 4
= TOF 7
c L 4
SOSE 4
2 E 150 keV 4
0 20 40 60 80 100
of fusion for Ar irradiation at the energies used in the experiment. Each peak is
dominated by the Ar-D—D chain contribution to greater than 99.2%.
°5 ‘s) 10 15 20 25 30 35 40 £45
of fusion for Xe irradiation at the energies used in the experiment. The high energy
tails are due to the Xe-Ti-D-D chain contribution.
200 keV Xe
Deuteron Energy (keV)
showing the contributions of the Xe-D-D and Xe-Ti-D-D chains.
5.4 Calculation of the Doppler Shift
center-of-mass (CM) frame. The energy of the proton in the lab frame is Doppler
shifted due to the velocity of the CM frame relative to the lab frame. To calculate
the energy of the proton in the lab frame given its energy in the CM frame, the
velocity of the CM frame and the angle between the CM velocity and the proton
(CM) velocity must be known. Given an angle 6 between the CM velocity and the
Up,lab = Vp,em + Bem (5.7)
2 2 . 2
\vp,tab] = ([Yp,em| + |vem| cos 8)” + (|vem|sin 8)” , (5.8)
where ¥p,1a5 is the proton velocity in the lab frame, vp,em is the proton velocity in
bee 1- (3
moc? +E
(relativistic). (5.9)
a single channel of the MCA spectrum. Relativistic velocity addition for conversion
to lab-frame velocity is not necessary since the maximum correction (~0.04%) is
too small to affect the observed spectrum.
before fusion calculated in Section 5.3, the lab-frame velocity distribution is found
using Eq. 5.9. Since the collision is between particles of equal mass, the CM velocity
is 1/2 of the lab-frame velocity.
the sample and total isotropy. An isotropic angular distribution would produce a
distribution of Doppler shifts symmetric around zero, i.e., positive and negative
shifts in velocity are equally likely. A unidirectional distribution would produce
the narrowest distribution of proton velocities. From the experimental data, an
isotropic angular distribution is inappropriate because the proton signal is not sym-
metric around 3.0 MeV (3.02 MeV minus the energy loss through the filter), and
the unidirectional distribution produces a proton signal that is too sharply peaked
compared to the experimental peaks. However, the experimental data appear to be
tributions would square the amount of information needed to be stored for each
atom of each chain, it was not possible to keep track of angular distributions in
the model calculations. Determining the precise angular distribution of the D-D
CM velocities requires quite complex convolutions of different angular distributions
in three-dimensional space for each nuclear collision from the initial entry of the
ion into the sample up to the fusion event. The number of possible collision se-
ries terminating with a given D energy is quite large, and all must be considered
to achieve a precise angular distribution. Such an analysis will not be attempted
here. Instead, an approximate angular distribution will be developed, which allows
a rough analysis of the experimental data in terms of the deuteron energy at the
transferrable from the incident ion will have a very narrow angular distribution be-
cause they are the result of head-on collisions, and therefore must be travelling in
likely it has been involved in nuclear collisions resulting in angular deviations. As-
suming a Gaussian distribution of angles centered around the incident ion direction
(which is 130° from the detector direction), the weight of the contribution of a given
angle @ is
where @ is in degrees, T is the deuteron energy at the time of fusion, and o(T) is
the standard deviation of the angular spread for energy T.
fusion less than the maximum value (Tmax) are nuclear and electronic energy loss of
the incident ion and atoms preceding the deuteron in the chain (AT; nuc, ATT ete), &
less-than-maximum energy transfer in the nuclear collision with the preceding atom
T= Tinax _ AT? nuc —_ AT) ete _ AT .o1 _ AT) nuc _ ATp ete . (5.11)
the nuclear stopping (collisions) terms are considered in calculating the angular
distribution of deuterons with energy T. The nuclear energy loss of the deuteron
accounts for less than 10% of its total energy loss for energies greater than 5 keV [3]
(the lowest deuteron energy which has a significant contribution to the total fu-
sion yield). Nuclear energy loss accounts for approximately 40% and 70% of the
total energy loss for Ar and Xe ions, respectively for the range of energies in this
experiment [3].
where M, and Mz are the masses of the incident and scattered particles, respectively,
E, is the energy of the incident particle immediately before the collision, and @ is
the angle between the direction of the incident particle before the collision and the
direction of the scattered particle after the collision. The equation can be inverted
Tmax i Tmax
unknown, a reasonable first-order approach is to combine all nuclear collision terms
together to give a characteristic scattering angle. For this approach, the standard
collisions. This functional form of o(T) is used with Eq. 5.10 to specify the angular
distribution.
distributions determined by Eq. 5.10, the proton energy spectrum is calculated by
setting up 1 keV wide bins for the proton energy, determining the bin into which
a proton produced by a certain combination of CM energy and angle will fall, and
adding the product of the angular weight and the energy weight to the bin. This
procedure is followed for the entire spectrum of energies and angles. The resulting
spectrum is then convoluted with the detected energy loss distribution of Section 5.1
irradiation), this transformation must be done separately for each chain because
distributions for 150, 300, 450, and 600 keV Ar and 200, 300, and 500 keV Xe
irradiations, treating Nny- as an adjustable fitting parameter. The best fits to the
experimental data for 600 keV Ar and 200 keV Xe are shown in figures 5.5a and 5.5b,_
respectively, with the area under the theoretical curves normalized to match that of
the experimental curves. The fits are compared to those assuming a unidirectional
distribution directly into the sample, i.e., @ = 130°.
Nnuc=93. For all Xe irradiations nruc=40 gives the best fit. The larger nny value
for Xe irradiations is consistent with the fact that nuclear stopping gives a larger
contribution to the energy loss of Xe than to that of Ar. Although fits to both
Ar and Xe data are rather good, the fits to Xe data are poorer than those to Ar
data, which is probably due to the more complicated collision chains involved in
producing fusion for Xe irradiation.
puted in the binary collision cascade model presented here, the calculated distri-
bution of deuteron energies coupled with the simple-minded approximation of the
angular distribution is sufficient to model the experimental proton signals accu-
rately. Similar fits to the triton and *He signals can be made, but the fits are
poorer due to the additional (unknown) energy distribution due to the energy loss
L ~ Model (@ = 1309 4
B00 / \ 4
L / \ a
wv 700 P / \ 7
S$ 600+ f \ 4
8 oot po
500 + ] \ 4
Cc i 4
2 400 L Mode Lan. \ _
eC 1 (33% Nuclear i * i”
QO 300 - Stopping) ; —
L 4 Experimental Data 4
200 + \ a 4
100- oy” ~— 4
8) i oe f l ! l Nu i i Stiameal ]
33% Nuclear Stopping) models and the experimental proton signal for 600 keV
Art? irradiation.
2800 2850 2900 2950 3000 3050 3100
irradiation.
depth distribution of fusion events from the *He signal, where the effects of depth
All Elements (Pergamon, New York, 1977).
in Solids, Vol. 1 (Pergamon, New York, 1985).
Hill, New York, 1968), Ch. 4.
TO MATERIALS ANALYSIS
rately (within ~10%) predicts the fusion yield for TiD,,7 irradiated with Ar and Xe
ions. Assuming the model accurately predicts fusion yields for arbitrary deuterium
concentrations, one should be able to irradiate a film of unknown deuterium concen-
tration and, using the experimentally obtained fusion yield, compute the deuterium
concentration based on the predictions of the model presented here. Thus, irradia-
tion of deuterium-containing materials with heavy ions could be used as a method
of determining the average deuterium concentration in the region within approxi-
mately 100 nm of the sample surface. The first two questions that come to mind
when considering the use of this technique for determining deuterium concentra-
tions are (1) how can the technique be optimized in terms of accuracy, simplicity,
and minimum detectable deuterium concentration, and (2) how would this optimum
technique compare with currently used methods.
Recoil Elastic Scattering (FRES), Secondary Jon Mass Spectrometry (SIMS), and
Nuclear Reaction Analysis (NRA) using beams of various ions in the MeV range
[1,2,3].
the sample with a hydrogen beam and detecting the simultaneous emission of pro-
sion of the analyzing beam (generally a few MeV) through the sample. The second
method involves glancing-angle incident beams of He and heavier ions with an en-
ergy of approximately 1 MeV/amu, and the detection of forward scattered hydrogen
or deuterium [5,6]. In this method, mylar or aluminum filters (~10-100 um thick)
must be placed in front of the detector to remove forward scattered incident ions.
Both techniques require the use of a standard to convert the spectrum to hydrogen
low-energy (100 eV to 10 keV) ion bombardment, can generally detect hydrogen
or deuterium down to concentrations of roughly 0.01 at%. However, accurate abso-
lute concentrations cannot be determined, even with the use of standards, because
of the severe effects of preferential sputtering, the effects of the matrix material
on the charge state of the emitted particles, and residual hydrogen in the vacuum
teristic energy of the nuclear reaction, can detect hydrogen or deuterium (depending
on the nuclear reaction utilized) down to approximately 0.1 at% (again, depending
on the reaction). Typical reactions used are 1H(19F,ay)!®O using 16-18 MeV 19°F
ions [7], and 'H(*'B,a)aa using 2 MeV 1!B ions [8] for hydrogen, and D(*He,p)*He
using 1.3 MeV *He beams [9]. NRA gives absolute measurements of the hydrogen or
deuterium concentration without the need for standards. However, the sensitivity
is limited by the fact that the signals are usually superimposed on a background
used, (3) insensitivity to hydrogen adsorbed during irradiation, and (4) there is
virtually no background in the region of the proton signal used for the analysis.
The disadvantages of using this method are (1) relatively low yields, (2) very little
deuterium concentration, the optimum ion and ion energy must be determined.
The goals to be considered, in order of importance, are (1) maximizing the fusion
yield, (2) minimizing the error created by dilution of the deuterium concentration
by addition of the irradiating species, and (3) minimizing the effect of the matrix
on the fusion yield. Fortunately, the three goals are not in conflict with each other.
yield, with a levelling off at the highest energies (due to the increase in the fraction
of energy lost to electronic stopping and the levelling off of the increase in the
fusion cross section). Also, the fusion yield for Ar is greater than that for Xe
(due to increased energy transfer to the deuteron). Theoretical fusion yields were
calculated for He, O, Ne, and Si at energies up to 1 MeV (Fig. 6.1). For energies
above 500 keV, Ar gives the highest yield. As the energy decreases, the highest
yield is obtained for lower mass ions. At the highest energy available to our ion
implanter (600 keV), Ar, Si, or Ne beams will give roughly equivalent fusion yields.
In that beams of inert gasses are easiest to obtain and have the largest currents on
10 -—T T T T T | | |
; q
| Ar 7
| pees eee si 7
| — Tose O° |
1Q71OL a |
ae, i A ,
wv i ,
° ee q - He a
E /; -_ 7 4
s 7 f L L |
~ fi “ 7
rok & 7
10 ah |
o's Li. | 1 | a ! ‘ | ! {
200 400 600 300 _
various ions.
sputtering coefficient. Thus, a higher dose of the lighter ion will be necessary to
sputter away enough material to expose the implanted ion profile to the surface and
dilute the deuterium in the region where a majority of the fusion events occur. Also,
the peak concentration of the lighter ion will be smaller than that of the heavier
ion due to increased range straggling. Therefore, if two ions of a particular energy
give roughly the same fusion yield, the lighter of the two will have a smaller error
due to the dilution effect. By the same arguments, a higher energy ion is preferable
considered. The presence of the matrix has two effects on the fusion yield. The
first is in its contribution to the stopping power of the incident ion J and energetic
recoils, which is easily calculated. The second is in the fusion events occurring in
chains in which it is involved, i.e., I-M-D-—D, etc. To take into account the effect
of these chains, the contribution to the total fusion yield for each chain must be
calculated, which greatly increases the complexity of the calculations required. The
ideal situation for ease of calculation of the fusion yield for a given irradiation is
for the direct I-D-D chain to dominate. In this case, only the fusion yield for the
I-D-D chain must be calculated. Therefore, to minimize the effect of the matrix and
simplify the theoretical calculation of the fusion yield, an ion should be chosen that
minimizes the transfer of energy to the deuteron via the J~M-—D chain. For titanium
deuteride samples, the fusion yield J-D-D dominates over all other chains for both
Ar (~99.2%) and Ne (~99.8%) irradiation for energies up to 1 MeV. Therefore, the
ure 6.2 shows the theoretical fusion yields as a function of deuterium concentration
in titanium deuteride for 1 MeV and 500 keV Ar and Ne irradiations. At 500 keV,
the yields for Ar and Ne are nearly identical for all deuterium concentrations. In
this case, Ne would be preferred due to its smaller dilution effect. At 1 MeV, the
Ar fusion yield is larger than that of Ne by a large enough amount to make Ar
detection limit of heavy-ion-induced fusion analysis is determined by the fusion
yield times the maximum dose of the irradiating ion that can be used without
significantly affecting the stoichiometry of the sample in the region of analysis (or
the maximum dose one is willing to use). Assume a 5 A beam current for two hours
(~2.5 x 10!” ions) to be the maximum dose. Assuming a precision of approximately
10% is desired, a minimum of 100 counts must be collected. For a detector solid
angle of 50 mSr and isotropic angular distribution of emitted protons, 25000 fusion
events must occur. This corresponds to a fusion yield of 1071%. If this value is taken
as the detection limit (for a 10% accuracy), the detection limit for 500 keV Ar or
Ne is approximately 4 at% in titanium. For irradiations at 1 MeV, the detection
limit is 3 at% for Ne and 2 at% for Ar. These values are somewhat higher than the
dict the fusion yield for Ar and Xe irradiation of TiD,.;. The above calculations
show that the method of measuring deuterium content by D—D fusion induced by
heavy-ion irradiation is expected to be on a par with other nuclear reaction analysis
methods in its ability to measure the average deuterium concentration within the
r 4
19719 q
o> [ J
c tou! — =
2 F 7
% : |
i E 4
-12
10°12 =
F ;
i |
L f 7
79°18 . ! a | r ! 1 I ma L t L
0 0.10 0.20 0.30 0.40 0.50 0.60
1 MeV and 500 keV Ar and Ne ions. The detection limit for 500 keV ions is 4 at%,
and for 1 MeV, it is 3 at% for Ne and 2 at% for Ar.
Scherzer, R. L. Schulte, E. J. Schneid, W. W. Magee, E. Ligeon, et al., Nucl.
Instrum. Methods 149, 19 (1978).
and their Applications (Academic, London, 1976).
demic Press, New York, 1978).
Technol. 14,492 (1977).
ions from reaching the detector, while allowing the fusion products to pass through
with as little energy loss as possible. The most penetrating of the backscattered
and sputtered particles created in this experiment are sputtered deuterons, which
can have a maximum energy of ~100 keV (for 600 keV Art* irradiation). A SisN4
layer 750 nm thick is required to full stop these particles.
The active area of the detector is a circle of 5.6 mm diameter (25 mm”). The filter
design is a 16.75 mm square of silicon (for easy alignment over the detector) with a
8 mm diameter circular window of Si3N,4 in the center. The diameter of the window
is large enough to avoid blocking the line of sight between any point on the sample
with a layer of Si3N4 produced by low-pressure chemical vapor deposition (LPCVD).
The thickness of the surface layer was determined by ellipsometry to be 940 nm.
A mask was designed to fit 18 filters on the wafer, each separated from the others
by a 100 ym scribe line for easy removal of the filters from the wafer (Fig. Al.1a).
Photoresist was spun onto the back side of the wafer, and the mask placed over it
so that the scribe lines were parallel to the (110) notch. The back side was then
exposed to ultraviolet light. The black region of the mask prevented exposure of the
photoresist, leaving it intact. The photoresist under the clear regions was exposed
was removed (Fig. Al.1c).
preferentially etches (100) Si. The etch is stopped by (111) planes. Therefore, the
etch walls will not be vertical, but will slope inward at ~35°. Thus, the scribe
lines do not etch all the way through the Si, but become groves. The diameter of
the circles in the mask were made to be 8.65 mm to insure an 8 mm circle on the
front side (Fig. Al.1d). The EDP etch was heated to 98°C and constantly stirred
using a magnetic stirrer. The etch rate was ~50 wm/hour and took approximately
ten hours to complete. After etching, the wafer was rinsed in de-ionized water and
very carefully blown dry with flowing nitrogen. Finally, the individual filters were
carefully separated. The finish filter is shown in figure Al.le.
etry. The layer composition was determined to be Si3N3 32, and the areal density to
be 5.25 x 1018 atoms/cm”, which corresponds to roughly 540 nm of Si;N4 assuming
SisN, 0.55 ym <
. vs Tete
3g oe Nt
FUSION YIELDS
for Ar and Xe irradiation of titanium deuteride. It is based on the analysis and
equations of Chapter 4. It is easily modified for use with other ions and/or other
targets. Explanations of the necessary modifications are given in the program list-
ing. It is set up so that the energy step AE is one thousandth of the incident beam
energy; however, since the fusion yield as a function of energy is quite smooth, only
every tenth of these thousand points are saved in the output file. The output file
is a series of 100 triplets of energy, fusion yield, and uncertainty (which has been
set to zero), as well as header information used by the plotting program NUFIT (a
descendent of NAGFIT). The input parameters are ion (Ar or Xe), ion energy, inter-
atomic potential (one of six choices), and deuterium concentration in the titanium
deuteride film.
maximum clarity of design. It is written in FORTRAN 4 and contains no machine
specific functions, other than input, output, and file structure. This version runs
about half as fast as the optimum version, which combines the calculation of several
120
130
140
irradiation of metal deuterides. Any ion or metal matrix can be
used (See note below). Fusion yields are calculated for the
summed to give the total fusion yield for the ion.
* To modify the metal matrix element modify Ma(1) and Z(1) and
* ons in the function delestp(E).
real*8 Ydd(2000) , Yidd(2000) , Yddd (2000) , Ymdd (2000),
+ Ytot (2000)
+ conv_e2 (3) ,conv_e3(3,2),conv_e4 (3,2) , gamma (3, 2)
real*8 delE,atfrac
xkxkkxk* (Differential Scattering Cross Section) ****x*x*x
m(1) = 0.311
m(4) = 1.0/3.0
m(5) = 1.0/3.0
format (' Enter the incident ion energy [keV]: ',$)
write (6,110)
write (6,130)
pi=3.1415926
Me=5 .485802E~-04 ! Electron mass in amu
Z(1)=22.0 ! Metal Matrix (Ti) - Atomic Number
Ma (1) =47.879 ! Mass (amu)
2(2)=1.0 ! Deuterium - Atomic Number
Ma (3) =39.948 ! Mass (amu)
I0 (1) =9.76+58.5/(Z(1) **1.19) ! Formula for Z2 >= 13 Bethe-Bloch
I0(2)=12.0+7.0/2(2) ! Formula for Z < 13 Bethe-Bloch
do 200 i=1,3
conv_e2 (i) =Ma (i) *Z (i) ** (4.0/3.0)
do 200 4=1,2
a(i,j)=0.8853*a0/(Z(i) **0.50 + 2(5)**0.50) ** (2.0/3.0)
conv_nl1 (i, j)=a (i,j) /(2(i) *Z (3) *e2* (1.0+Ma (i) /Ma(4)))
conv_n2(i,j)=2.0*pi*a(i, 4) *Z (i) *Z(4) *e2/(1. 0+Ma (j) /Ma(i))
conv el (i, j)=1.216091*Z (i) **(7.0/6. 0) *2(5)/
conv_e3(i, j)=4. 0*Me/ (Ma (i) *2 (4) *10 (4) )
conv_e4 (i, j)=8.0*pi*e2**2 .0*Z (i) **2.0/10 (4)
gamma (i, j)=4. O*Ma (i) *Ma (3) / ( (Ma (i) +Ma (3) ) **2.0)
continue
** characteristic energies **
E_m_max=E0*gamma (3,1) ! Max Metal energy (eV)
Ed | Max=max (EO*gamma (3,2),E_m_max*gamma (1,2) ) !Max D energy (eV)
delE (1) =E 1 m | max/float (loop) — ! Energy step for M ions (eV)
delE (2) =E | ~d | max/ float (loop) ! Energy step for D ions (eV)
delE (3) =E0/float (loop) ! Energy step for I ions (eV)
stp = epsilon _D
atfrac(2) = eta_D
Ydd(1) = atfrac(2) *fcs (delE(2)) *delE(2)/stp
do 250 i=2,1loop
continue
kkk kkk kKaKKKKKK
xx First generation recoils **
call
call
call
call
call
kk
call
call
call
xk
call
Ytot (i)= Yidd(i) +
fuse (1,2, Yddd, Ymddd)
fuse (3,2, Yddd, Yiddd)
M-D-D~-D
I-D-D-D
Yield
Yield
M-M-D-D
I-M-D-D
fuse (1,1, Ymdd, Ymmdd)
fuse (3,1, ¥mdd, Yimdd) !
Yield
Yield
Yield
fuse (3,2, Ydmdd, Yidmdd) ! tI
fuse (3,1, Ymddd, Yimddd) 1 I~
fuse (3,1, Ymmdd, Yimmdd) !r
K*
fuse (1,1, Ymmdd, Ymmmdd) !
fuse (3,1, Ymmmdd, Yimmmdd) !
-~M-D-D Yield
Yiddd(i) + Yidddd(i) + Yidmdd(i) +
Yimdd (i) + Yimddd(i) + Yammdd(i) + Yimmmded (i)
call
call
call
call
call
call
call
call
call
call
call
call
cali
call
call
call
call
stofus (fileout, 3, Yidd,
titler('Iddd',4,labl,ilen2, fileout)
stofus (fileout, 3, Yiddd,
titler('Idddd',5,labl,ilen2, fileout)
stofus (fileout, 3, Yidddd,
titler('Itidd',5,labl,ilen2, fileout)
stofus (fileout, 3, Yimdd,
titler ('Ititidd',7,labl,ilen2,fileout)
stofus (fileout, 3, Yimmdd,
titler('Itititidd',9,labl,ilen2, fileout)
stofus (fileout, 3, Yimmmdd,
titler('Itiddd',6,labl,ilen2, fileout)
stofus (fileout, 3, Yimddd,
titler('Idtidd',6,labl,ilen2, fileout)
stofus (fileout,3,Yidmdd,
titler ('Ytot',4,labl,ilen2, fileout)
stofus (fileout,3, Ytot,
KKK KKK KKK KKK KEK KKK KKK KK KKK KKK KKK KKK KEK KEK KEKE KKK KKK KEKE KKK KK KKEKKEKKEKKK
* eV Angstrom*2/atom for ion (ion) of energy (energy) (eV) ina *
* target of M(1)D(xd). The formulae used are from J.P. Biersack, *
* E. Ernst, A. Monge, and S&S. Roth, Tables of Electronic and *
* Nuclear Stopping Powers, and Energy Straggling for Low Energy *
* Ions (Han-Meitner, Berlin, 1975)p. 4 *
* epsi_m = reduced mass for collision with metal *
* epsi_d = reduced mass for collision with deuteron *
* Sn m = nuclear stopping in pure metal *
* Sn d = nuclear stopping in pure deuterium *
KOKI RO OK IOI OK ROI OO KR KOK II KK KK IO KR OR IR IO IO OR Kk OR KOK Kk KK
+ conv_e2 (3), conv_e3 (3,2), conv_e4 (3,2) , gamma (3, 2)
epsi_m=conv_nl(ion,1)*energy
epsi_d =conv_nl (ion, 2) *energy
xnucstp=(Sn_m + xd*Sn_d)/(1.0+xd) ! Addition by Bragg's Rule
return
* of eV Angstroms*2/atom for ion (ion) of energy (energy) (eV) *
* ina target of M(1)D(xd). The formulae are from the same ref. *
* as the nuclear stopping power. *
* S1(i) = Lindhard-Scharff formula electronic stopping for *
* stopping in (i=1) metal and (i=2) deuterium *
* Sb(i) = Bethe-Bloch formula electronic stopping for *
* stopping in (i=1) metal and (i=2) deuterium *
* Se(i) = Interpolation between L-S and B-B stopping *
* conv_e2(ion,i) = energy below which electronic stopping *
* is adequately described by S1(i) alone *
* epsi_b = 'reduced' Bethe-Bloch energy *
* See Eqs. 1.3, 1.4, and 1.5 of thesis *
KKK KKK KR KEK KKK KEK KK KKK KK KKK KEKEKE KEK KEKE KK KEK KEK KKK KKK KEK KKK KKK KKEKKKKK
real*8 conv_nl,conv_n2,conv_el,conv_e2,conv_e3,conv_e4
real*8 xd,a,gamma
common /infol/ xd,a(3,2),conv_n1(3,2),conv_n2(3,2),conv_e1(3,2),
+ conv_e2 (3), conv_e3(3,2),conv_e4 (3,2), gamma (3,2)
do 200 i=1,2
$1(1)=conv_el (ion, i) *energy**0.50
if (conv_e2(ion) *energy .gt. 10.0) go to 100
Se(i)=S1(i)
go to 200
continue
epsi_b=conv_e3(ion,i) *energy
Sb (i) =conv_e4(ion,1i) *log(epsi_bt+1.0+5.0/epsi_b)/epsi_b
Se (i)=1.0/(1.0/81(i)+1.0/Sb(i))
continue
elestp=(Se(1) + xd*Se(2))/(1.0+xd) ! Addition by Bragg's Rule
return
end
function delestp (energy)
* of eV Angstroms*2/atom for deuterons of energy (energy) (eV) *
* ina target of M(1)D(xd). Coefficients obtained from H. H. *
* Anderson and J. F. Ziegler, Hydrogen Stopping Powers and *
* Ranges in All Elements (Pergamon, New York, 1977). These are *
* best fits to experimental data. *
KKK KKK KK KKK KKK KKK KEE KK KKK KK KEK KE KKK KKK KEK KK KKK KKK KKK KKK KE KKKKKEKEKKEKEKK
real*8 conv_| nl; conv_| n2, conv_ el, conv | e2, conv_e3,conv_e4
reak*8 xd,a,gamma
common /info1/ xd,a(3,2),conv_ni(3,2),conv_n2(3,2),conv_el(3,2),
+ conv e2 (3), conv_e3 (3, 2), conv 24 (3, 2), gamma (3,2)
E=energy/ (2.01594*1000.0) ! E in units of keV/amu
if (E .ge. 10.00) go to 200
Se d = 1.262* (E**0.50)
Se _ti= 4.862* (E**0.50) ! in Units of 1E-15 eV cm*2
go to 300
continue
Sl_d =1.45* (E**0.45)
Sh dad =242.6*log({1.0+(1. OE+4/E)+(0. 1159*E))/E
Se d =1.0/(1. 0/Si_d + 1.0/Sh_a)
Sl_ti=5.496* (E**0.45)
Sh_ti=5165.0*log(1.0+(568.5/E)+(9.474E-3*E) ) /E
Se ti=1.0/(1.0/S1_ti + 1.0/Sh_ti) ! in Units of 1E-15 eV cm*2
continue
delestp=10.0*(Se_ti + xd*Se_d)/(1.0+xd)! in Units of eV A*2/atom
return
end
KK KKK KKK KEK KKK KEK KK EK KEK KK KK KK KEKE KKK KKK KKK KEK K KEKE KEKE KKKKEKKKE KK KKK
function dscs(ion,E,itarg,U,i)
* This gives the differential scattering cross section in units
of Angstrom*2/eV for an incident ion (ion) of energy E (eV)
to collide with an atom itarg and give it energy U (eV).
Formula is from P.D. Townsend, J.C. Kelly, and N.E.W. Hartley,
Ion Implantation, Sputtering and Their Applications (Academic,
London, 1976) pp 19-21. The fitting parameters lambda,m,q are
obtained from K.B. Winterbon, Rad. Eff. 13 (1972) 215.
* See Eq. 4.8 of thesis [conv_nli(ion,itarg) = c_r]
FORO OR IOI OOO OOOO IO FOR OI OI II IO IOI IO I OIE RO IO Ik kok
real*8 t,E,U,dscs
real*8 lambda,m,q
common /coef/ lambda(6),m(6),q(6)
real*8 conv_ni,conv_n2,conv_el,conv_e2,conv_e3,conv_e4
real*8 xd,a,gamma
common /infol/ xd,a(3,2),conv_n1(3,2),conv_n2(3,2),conv_e1(3,2),
+ conv 22 (3), conv 23 (3, 2), conv “e4 (3, 2), gamma (3, 2)
t=conv_ni{ion, itarg) **2. 0*E*U/garina (ion, itarg)
dscs= (3.1415926/2.0) *a(ion, itarg) **2.0*lambda (i) * (t** (-m(i))) *
+ ((1.04+(2.0*lambda (i) *t** (1.0-m(i))) **q(i)) ** (-1.0/q(i))) /U
return
end
KR KKK KKK KKK KKK KKK KKK KK KEK KKK KKK KEK KKK KKK KKK KKK KK KKK KKKKKKKE KEKE KKEKKEKKKKK
function fcs(E_ lab)
* This gives the nuclear fusion cross section for a deuteron
with an energy E_lab (eV) in the laboratory frame of fusing
with a stationary deuterium atom in the target by the reation
D(d,p)T using the approximation S(E)=SO + S1*E + 0.5*S2*E*2.
Units of the cross section are Angstrom*2. S{(E) parameters
taken from A. Krauss, H.W. Becker, H.P. Trautvetter, and C.
st ee FH HH HF
+ + + HH
* See Eq. 4.7 of thesis *
KR KKK KKK KE KKK KK KEKE KKK KK RK KEKE KKK KKK KK KEKE KEKE KEKEKKKKKKKKK KKK KK KKK KKK
real*8 b,S0,S1,S2,E_cm,E lab, fcs
fcs=(SO0+S1*E_cm+0.50*S2*E_cm**2.0) *exp (-b/E_cm**0.500) /E_cm
KKK KK IKK KKK KKK KKK KK KKK KKK KKK KKK KKK KKK KKK KEKE KKK KKKEKKKKEKKK
* SUBROUTINE FUSE *
using iterative Eq. 4.10 of thesis, where:
atfrac(itarg) = eta_b
+ conv_e2 (3), conv_e3 (3,2) ,conv_e4 (3,2) ,gamma (3,2)
real*8 delE,atfrac
delU = delE(ion) *gamma(ion,itarg) /float (m)
sum = 0.00
do 100 j=1,n
continue
if {ion .ne. 2) stp=xnucstp(ion,delE (ion) )+telestp (ion, delE (ion) )
if (ion .eq. 2) stp=xnucstp (ion, delE (ion) )+delestp (delE (ion) )
Yout(1) = atfrac(itarg) *sum*delU*delE (ion) /stp
E = float (i) *delE (ion)
m = int (E*gamma (ion, itarg) /delE (itarg))+1
delU = E*gamma(ion,itarg) /float (m)
sum = 0.00
do 200 j=1,m
U=float (j) *delU
ni=int (U/delE (itarg) +0.50)
sum = sum + Yin(n1)*dscs(ion,E,itarg,U,ipot)
continue
if (ion .ne. 2) stp = xnucstp(ion,E) + elestp(ion,E)
if (ion .eq. 2) stp = xnucstp(ion,E) + delestp(E)
Yout (i) = Yout(i-1) + atfrac(itarg) *sum*delU*delE (ion) /stp
continue
* SUBROUTINE LABELS *
label to be appended to the file names to differentiate
between different runs of the program.
if (xchar(i:i) .eq. ' ' .and. key .eq. 1) go to 200
if (xchar({i:i) .ne. ' ' .and. key .eq. 0) ibeg=i
if (xchar(i:i) .ne. ' ') key=1
* SUBROUTINE TITLER *
tion '.fit' to each output file.
character fileout*30, file*22,lab1*4
itot=ilenl+ilen2+4
* SUBROUTINE STOFUS *
in a form readable by NUFIT. For convenience, the uncer-
tainty in the yield values is stored as zero. To conserve
space, only every tenth value is stored. As the yields
are smooth functions of energy, no significant info is
lost.
real*8 Y(2000),E
open (unit=1, status='NEW', file=fileout)
delY=0.000000E+00
1010
1020
1030
1040
E=delE (ion) *10.0*float (i) /1000.0
write(1,1050) E,Y(1I*10),delyY
x-axis label
yraxis label