DEPTH PROFILING OF LOW ENERGY IONS IMPLANTED INTO METALS
USING THE FIELD ION MICROSCOPE/IMAGING ATOM PROBE
SCOTT DOUGLAS WALCK
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
To my wife and son, Karen and Adam Walck,
and my mother, Drucilla Linn
The author wishes to thank the members of his supervisory committee:
Dr. Christopher D. Batich, Dr. Robert T. DeHoff, Dr. Paul H. Holloway,
and Dr. Gary G. Ihas. This author is extremely grateful to his advisor
and friend, Dr. John J. Hren, who furnished an atmosphere in which the
author was allowed to find his own way and discover his full potential.
There are several members of the field-ion community without whose
help and assistance the FIM/IAP at the University of Florida could not
have been built. The author is deeply indebted to Dr. John A. Panitz of
Sandia National Laboratories, whose generosity in terms of advice, aid,
and criticisms to a struggling graduate student is nothing short of
remarkable. The author also wishes to thank Dr. Gary G. Kellogg, also of
Sandia Laboratories, for his advice and many stimulating discussions.
Many thanks go to Gerry Fowler and Larry Karkeweitz, who shared with the
author the knowledge of the details of the FIM/IAP instrumentation.
Encouragement from Dr. Sidney S. Brenner of the University of Pittsburgh
and the learning experience that he jammed into three months is greatly
appreciated. Dr. Michael K. Miller of Oak Ridge National Laboratories is
also thanked for his technical and scientific discussions.
Many technical and support groups at the University of Florida
should also be thanked. Dr. Anthony Buonoquisti is thanked for the many
fruitful discussions and scholarly advice he has given over the years.
Machinists Ralph Jones and Herman Bailor were indispensable with respect
to designing and building the FIM/IAP. Many thanks go to Robert Owen
whose late night discussions and help with electronics made impossible
tasks a little easier. Mr. Don Sanford in the Department of Physics is
thanked for his help in designing the new FIM/IAP specimen holder and
TIG-welding the copper braid. The author wishes to extend thanks for the
technical assistance given to him by Dan Steadham and Temel Buyuklimanli.
He also expresses his gratitude to his fellow students who shared the
same boat and helped to infuse into this degree some of the philosophy
that goes with it. The author would like to thank the local chapters of
the American Vacuum Society in Florida and New Mexico for the scholar-
ships they have given him to attend meetings and short courses which were
invaluable to him with respect to his research progress. Special thanks
go to Norman Parsons of the Florida Chapter for his efforts to help the
The author also would like to thank Tektronix employees: Dave
Jackson, Bob Messer, John Loggee, and Richard Knapp for solving and
helping to get the Tektronix equipment on-line as an integral part of the
Imaging Atom Probe. They were invaluable in solving both software and
hardware problems. These gentlemen not only stand behind their product,
but represent the Tektronix motto, "Committed to Excellence."
The author wishes to thank the Department of Energy for funding of
this effort. Gratitude is also extended to the University of Florida
College of Engineering for the SEED money to start the project, the Major
Analytical Instrumentation Center (MAIC) for technical and instrumental
support, and the Department of Materials Science and Engineering for
supporting the author on the Center of Excellence program for an extended
period of time.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . .
ABSTRACT . . .
LITERATURE SURVEY .
Introduction . .
FIM Principles . .
Field Ionization . .
Field Evaporation .
Atom Probery . .
Applications . .
Field-Induced Stresses .
Microstructure Of Implanted Metals .
Hydrogen In Metals . .
Hydrogen Embrittlement .
Trapping Of Deuterium .
Nitrogen Implantation In Metals .
Tribological Studies .
Ion Beam Carburization .
Applicability Of FIM Techniques To
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
Nitrogen In Metals
INSTRUMENTATION . . .
Field Ion Microscope/Imaging Atom Probe (FIM/IAP)
FIM/IAP Description . .
Chamber . . .
Sample Holder . .
General Description Of The IAP .
TOF Mode . . .
Time-Gated Mode . .
Computer And IEEE-488 Instrumentation .
7912AD . . .
Scientific Instruments 5500 .
Bertan 205A-30R . .
IAP Data Collecting And Handling Programs . 55
Ion Gun . . 58
Mass Identification in the Colutron Ion Gun . 65
Transmission Electron Microscopy . 67
FIM/IAP "Bulk" Holder . . 68
FIM/TEM "Double-Tilt" Holder . 70
FIM/TEM "Field-Effect" Holder . 72
EXPERIMENTAL CONSIDERATIONS . . 79
Depth Profiling Using The FIM/IAP . 79
Ring Counting Experiments . . 80
Specimen Geometry . . 82
IAP probed-volume considerations . 84
Volume calculation . . 85
Determination of 0 . 89
Determination of KD for nickel . 91
Experimental procedure . 92
Determination of geometric parameters . 101
Calculated curve . . .. 105
Sample selection criteria . 105
Effects Of Field Ionization Imaging And Evaporation 112
Field Induced Stresses . . 112
Field Evaporation Observations ... .... 118
Dependency of evaporation field on imaging gas 118
Implantation lowering of evaporation field 119
Low field desorbed species . 120
He signal . . .. 122
Special Problems Associated With Hydrogen/Deuterium 123
The Deuterium Background (Di) 124
Deuterium Implantation Conditions . 129
RESULTS OF IMPLANTATION EXPERIMENTS . . 132
Specimen Preparation .. . 132
Nitrogen Implantation In Nickel . . 134
Nitrogen Implantation In Tungsten . 148
Deuterium Implantation In Nickel . 159
Carbon In Tungsten And Nickel . . 167
DISCUSSION OF RESULTS . . 172
Instrumentation . . . 173
FIM/IAP . . . 173
FIM/TEM Specimen Holders . . 175
Methods/Techniques . . 175
Discussion Of Experimental Results . 177
Control Experiments . . 177
Field effects . . 178
Ring counting experiments . 179
Automated data collection . 179
Background gases . . 180
Deuterium background . . 181
Nitrogen Implantation In Nickel . 183
Nitrogen Implantation In Tungsten . 186
Applicability Of The TRIMML Code To Low Energy Ions 189
Reproducibility Of Profile Results . 189
Curve shapes and total ions detected . 189
Error analysis of geometric model . 191
Deuterium Implantation In Nickel . ... 192
Carbon In Tungsten And Nickel . ... 194
CONCLUSIONS . . . 196
Depth Profiling Techniques . . 197
Field-Induced Stresses . . 198
Nitrogen Implantation . . 200
Nitrogen In Nickel . . 200
Nitrogen In Tungsten . . 200
In Situ Implantation Results . . 201
Deuterium Embrittlement Of Nickel . 202
FIM/IAP Observations . . 202
SUGGESTED FUTURE WORK . . 204
Nitrogen In Nickel . . 204
Nitrogen In Tungsten . . 205
Carbon In Metals . . 205
Deuterium In Metals . . 206
Deuterium Implanted Nickel Emitter Failure . 206
Deuterium Redistribution . . 208
Cryogenic/room temperature experiments 208
Temperature-controlled experiments . 209
Field-Induced Stresses . . 210
Implantation Depths . . 211
Orthogonal Axis Implantation . . 212
Implantation Lowering Of Evaporation Field . 213
IMPROVED FIM SPECIMEN HOLDER WITH TEMPERATURE CONTROL 215
ALIGNMENT OF THE COLUTRON ION GUN . . 218
MEASURED TIME DELAYS . . . 222
FIM/IAP TEK BASIC PROGRAMS . . 225
IAPRING.HV . . . 225
IAP2TAPE . . . 246
PEAKPICKOFF.FAST . . 268
PEAKCUMULATOR . . . 274
DATAREDUCER . . . 275
CUMVSRING . . . 280
FIMSUPPLY . . . 286
TIPREDUCER . . . 291
PROFILER . . . 296
INDEXED FIM MICROGRAPH MONTAGE . . 305
RFERENCES . . . 307
BIOGRAPHICAL SKETCH . . .
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of
the Requirements for the Degree of Doctor of Philosophy
DEPTH PROFILING OF LOW ENERGY IONS IMPLANTED INTO METALS
USING THE FIELD ION MICROSCOPE/IMAGING ATOM PROBE
Scott Douglas Walck
Chairman: John J. Hren
Major Department: Materials Science and Engineering
The implantation depth is an important parameter if properties are
to be modified in a controllable and reproducible fashion by ion
implantation. The Field Ion Microscope/Imaging Atom Probe (FIM/IAP) is
superb for depth profiling, having depth resolutions on the order of a
crystal lattice spacing of the metal under investigation. This study
involves the application of the FIM/IAP in obtaining depth profiles of
low energy ions (<20 keV) implanted into metals.
Two technologically important ion species were used, nitrogen and
deuterium. It was shown that the deuterium partial pressure was not a
problem when a properly differentially pumped ion gun was used. Specific
problems of applying FIM/IAP to these species were reported. The results
of nitrogen implanted into nickel showed that the nitrogen resists field
evaporation even though the nickel was removed. Range and straggling
values for nitrogen implanted into tungsten with energies of 2.5-9 keV
were found and compared to Monte Carlo computer calculations.
Two special Transmission Electron Microscope (TEM) sample holders
were developed for use with FIM specimens. Using these holders, it was
shown that there was little or no influence of the high electric field on
the implanted defect microstructure of the specimen. However, nickel was
seen to be embrittled by deuterium implantation, but not by helium or
The use of TEM was critically important in obtaining the geometric
parameters used to determine a depth scale from implanted emitters
profiled under ultra-high vacuum conditions. The volume probed was
related to the cumulative matrix signal. The geometric parameters were
used to obtain the proportionality constant between the cumulative matrix
signal and the probed volume (a function of depth).
Several critical observations for proper interpretation of FIM/IAP
results were reported. Foremost of these was the lowered evaporation
field of implanted emitters. This study established a methodology for
applying the FIM/IAP to the depth profiling of ion implanted species into
In the field of materials science, there is a wide range of interest
in the use of ion implantation. This interest extends from basic and
applied research to commercial applications. Ion implantation has been
used extensively in semiconductor processing for a number of years.
Recently ion implantation is proving to be highly beneficial in the
modification of surface properties of certain alloys. Reduced friction
and wear and/or increased corrosion resistance have been reported in tool
steels, cemented carbides, and titanium-based surgical prosthesis alloys.
Radiation damage in alloys caused by the hostile environments of nuclear
reactors has long been simulated by ion implantation. Ion implantation
can cause amorphization of surface regions and impart special properties
or created supersaturated concentrations of insoluble species not
achievable by conventional methods. In fact, it can provide an almost
limitless modification of surface composition, allowing the formation of
phases and compositions without regard to thermodynamic stability.
The implantation depth is an extremely important parameter when ion
beams interact with metals. Very little data are available for the
ranges of light, low energy (<40 keV) ions into metals; conventional
analytical techniques such as secondary ion mass spectrometry (SIMS),
nuclear reaction analysis (NRA) and Rutherford backscattering (RBS)
suffer from a limited spatial resolution for the shallow depths.
Although it is not widely recognized outside the FIM community, the atom
probe and imaging atom probe are superb for compositional depth
profiling. With an imaging gas present, depth resolutions of one atomic
plane are expected. The imaging atom probe (IAP) has several advantages
over the conventional atom probe (AP) for profiling: 1) it offers a
larger area of analysis (approximately 102-103 larger), 2) crystallo-
graphic effects are minimized, 3) a complete mass spectrum is collected
with each pulse, and 4) all atoms within the probed volume will strike
the detector. However, there are two disadvantages in using the IAP.
The IAP employs an extremely short flight distance (z.15m) as compared to
the AP (=lm) and mass resolution suffers accordingly. Because of this,
material systems must be chosen such that the mass-to-charge ratios are
sufficiently resolved temporally. The other disadvantage is the
difficulty in the determination of ring collapses under ultra high vacuum
(UHV) conditions (i.e. no imaging gas present). In the AP an increase in
signal occurs when the edge of a ring sweeps by the probe hole [1,2].
(See below for a discussion of the AP.) This periodic increase
corresponds to the collapse of a ring and can be used to assign the depth
scale. In the IAP, distinguishing between an increase in signal and an
increase due to a voltage increase is difficult to do because the signal
from a single set of planes is small compared to that coming from the
entire probed surface. This particular disadvantage will be discussed in
detail and a solution put forth.
This study involves the application of the IAP toward the depth
profiling of nitrogen and deuterium into field emitters. Specific
instrumental problems will be addressed. These include those attributed
directly to implantation into field emitters and those associated
specifically with the implanted species. Deuterium and nitrogen are the
primary implantation ions used in this study. The study of the
interaction of hydrogen and its isotopes to defects in metals may well be
one of the most important problems in materials science. A full
understanding of the trapping of hydrogen at defects is essential for the
operation of future fusion reactors. Essentially all of the energy
sources of tomorrow will have hydrogen interacting in some way with the
materials system. Nitrogen is now playing a major role in the surface
modification of commercial alloys. Nitrogen, sometimes in conjunction
with other elements such as boron and titanium, is the most widely used
element for modifying surface properties by ion implantation. The
advantages of ion implantation over conventional methods of surface
treatment include relaxed heat treatment requirements, stability of final
shape, controlled composition with depth, and the possibility of creating
beneficial metastable phases.
Although the effects that deuterium has on materials may be
deleterious and those of nitrogen may be beneficial, finding the range
for low energies of these elements is a common problem. Each has
particular instrumental difficulties which arise when the IAP is used to
analyze for them. These difficulties will be discussed and solutions
presented for overcoming them. A knowledge of the complexities for
implanted nitrogen and deuterium in applying the IAP to studying them
will be invaluable for its general use to other types of ions. Many of
the problems for these interstitial-type species (i.e. nitrogen and
deuterium) will not be present for substitutional-type elements, but it
is essential that the experimentalist be aware of the potential problems
when a new system is first investigated.
The rest of this chapter will be divided into four main sections: 1)
a brief introduction to FIM principles, techniques, and terminology,2)
the microstructure of implanted specimens, 3) a literature survey of
hydrogen in metals, and 4) a literature survey of nitrogen implanted in
This section will be used to describe some of the fundamental
aspects of FIM techniques for the reader who is not thoroughly familiar
with them already. For a more complete discussion of FIM theory and
practices, several excellent books are available. The three which this
author recommends are: 1) Field Ion Microscopy edited by Hren and
Ranganathan [31, 2) Field Ion Microscopy, Principles and Applications by
MUller and Tsong , and 3) Field Ion Microscopy in Materials Science by
Wagner , The last of these is the most recent and includes operating
principles of both the atom-probe and imaging atom probe types of
A basic FIM in comparison with today's sophisticated instruments is
relatively simple. It employs no lenses, no primary beam, and requires
no high power consumption. It consists of a vacuum chamber (usually
UHV), a cryogenically cooled specimen holder that can be biased to a high
voltage (0-20 kV), and a leak valve which allows backfilling of the
vacuum with an inert gas such as helium or neon to a pressure of
approximately 1x10-5 Torr. Figure 1-1 shows a schematic of a basic field
ion microscope. The specimen is normally electrochemically polished to
an emitter endform (having a radius of curvature of about 200 to 1000 A)
When a voltage is applied to it in the microscope, the shape of the
emitter causes a high electric field that ionizes the gas molecules
(field ionization) above the surface step sites where the planes of atoms
emerge at the surface. The ionization process is due to quantum
mechanical tunneling of an electron from the gas atom through a potential
barrier between the metal surface and the atom. The ions are then
repelled away from the positive tip and strike a phosphor screen assembly
(a channel electron multiplier array (CEMA)/phosphor screen combination)
where the image is photographically recorded. This process is
illustrated in Figure 1-2. Besides the apparent resolution of the image,
crystallographic information can be obtained directly, i.e. without
diffraction, but lattice parameter information cannot.
When the voltage is raised such that the fields exceed those
normally used for imaging conditions, the atoms themselves can be
positively ionized (termed field evaporation). This process can be
considered to be the result of the electric field lowering the energy
barrier for sublimation of the surface atoms. Because of this, field
evaporation is a thermally activated process. Every metal has a
characteristic field evaporation strength which is also a function of
Schematic diagram of a simplified field ion microscope.
/ ^/ /f/' ^Surface
/ / FIELD ION TIP ,S a
Figure 1-2 Schematic diagram of the filed ionization process. The gas
atom is polarized by the high electric field and is attracted towards the
tip, strikes the cold surface several times, loosing some of its kinetic
energy each time. At a critical distance above an ionizing site the gas
atom looses an electron to the metal by a quantum mechanical tunneling
process and is repelled from the tip towards the viewing screen where the
image is photographically recorded.
temperature. The process of field evaporation can be controlled very
precisely by varying either the applied field with the voltage or by
changing the specimen temperature, and forms the basis for AP instru-
ments. Atom probe instruments rely on one of these two methods to
initiate field evaporation in a very short time in order for the ions to
be measured temporally at a detector, thus forming a time-of-flight (TOF)
mass spectrometer. A high voltage pulse with a subnanosecond risetime
and 10-20 nsec width and having an amplitude of 1-3 kV is used in the
conventional AP and imaging atom probe (IAP). The pulsed-laser atom
probe (PLAP) is basically an IAP employing a nitrogen laser to
instantaneously heat the surface of the emitter to cause field
evaporation. The latter instrument enjoys the benefits of a reduced
electric field and the capabilities of analyzing specimens with poor
electrical conductivities, such as silicon, and glasses. Because the
removal of atoms from the surface of the emitter is seen as a collapse of
the characteristic rings which form the FIM image, depth resolutions of
one atomic plane are expected.
It should be noted that field evaporation is the final step in the
specimen preparation technique. When the voltage is applied for imaging
in the FIM, local protuberances are field evaporated. The tip continues
smoothing in this manner until the ring structure appears, and a stable
image occurs. A particular radius of curvature can be "dialed-in" by
continued field evaporation from the "as-polished" condition to a preset
voltage which corresponds to that radius at the given temperature,
providing, of course, that the initial radius is less than that of the
The conventional AP is designed with a 1-2m flight tube behind a
CEMA/phosphor screen assembly that has a 4-6mm hole through it. Surface
atoms which are aligned with and pass through this probe hole are then
focused with an einzel lens to strike the detector. Electronic timing
circuits interfaced with a computer are used to determine the flight time
which in turn is used to calculate the mass to charge ratios. The
detector most often used is a Chevron assembly, constructed using two
CEMA's. The mass resolution, M/AM, of the AP is on the order of 200 .
The source of the poor resolution is due to energy deficits inherent in
the field evaporation process . The energy-compensated AP uses a
Poschenreider lens  to increase the resolution to as high as 5000 .
In both instruments the apparent size of the probe can be changed by
varying the tip to screen distance. Compositions of precipitates with
dimensions on the order of 10 A have been analyzed routinely. In
addition, since the AP is a TOF instrument, all elements can be detected,
including isotopes of hydrogen. It should be noted that the metallur-
gical applications of the AP did not advance at a rapid pace until the
widespread use of fast electronics and computerized interfacing allowed
the collection and reduction of large number of data. The early AP's
employed a storage scope with the results of each trace needing to be
analyzed by hand.
The IAP (and PLAP) are constructed with a Chevron assembly (which
can be curved) mounted .1-.15m from the tip. The assembly is used as a
detector and viewing screen. Since the IAP has such a short flight
distance, extremely fast digitizing scopes are employed to capture the
resulting waveforms. The IAP, although having poor mass resolution
(=50), does have the advantages of having a full spectrum result with
each pulse and a large probe area (the entire imaging surface). The
Chevron assembly can be gated to be turned "on" to coincide with the
arrival a particular mass at the detector. In this mode of operation,
the results of many pulses are integrated photographically to form a
time-gated image. The resulting image can be compared with the FIM image
in essentially the same way as an X-ray elemental map is compared to a
SEM micrograph. The results can be very dramatic, for example showing
the segregation of impurities to grain boundaries . For metallurgical
applications, the AP and IAP together in one instrument can be a powerful
The FIM/IAP also suffers no problems of minimum detectability. In
principle, it has single-atom detectability. Another important point to
be made is that the IAP resolves deuterium from other low-mass peaks such
as H* and He+ very well, despite the flight distance being extremely
short (.15 m).
The FIM and AP techniques are being applied to diverse areas of
interest. The atomically clean surface of an emitter caused by field
evaporation make them attractive techniques for surface science
applications. Studies are being done in the areas of surface segrega-
tion, surface diffusion, adatom adsorption, precipitation, radiation
damage, radiation-induced precipitation and catalysis. Segregation of
elements to interfaces are the forte of the AP. Many different materials
have been examined, including: steels, nickel-based superalloys,
aluminum-copper alloys including those which develop Guinier-Preston
zones, alloys which undergo order-disorder transformations, glasses, and
semiconductors. The review by Wagner discusses in detail the fundamen-
tals and applications of FIM techniques in materials science .
FIM techniques are by no means the solution to everyone's problems.
Not all specimens that one would like to examine in the FIM can be
prepared into the required shape. And if they can, it doesn't mean that
they will withstand the effects of the high electric fields. One major
disadvantage of FIM techniques is the extremely small volume of material
which can be examined. The volume of a field emitter examined is on the
order of 100 times smaller than that of a TEM specimen. This means that
finding features of interest, even with the aid of TEM, can be quite
difficult and care must be exercised when interpreting results from such
a small sampling.
Also of primary importance to the success of applying FIM techniques
to the study of implanted species with defects is the influence that the
high electric field has on them. Extremely high tensile and shear
stresses are induced within the emitters due to electrostatic (coulomb)
forces present at the surface of the emitters. These stresses can be
visualized by imagining a sphere of the same radius of curvature as a
field emitter to which the same voltage is applied (Figure I-3a). The
stresses induced in this imaginary sphere are purely tensile and at the
surface are equal to F2/8n where F is the electric field at the surface.
The electric field is equal to V/r, where V is the applied voltage and r
is the radius of the sphere. Within the volume of this sphere, there is
gure 1-3 Field distributions for various shaped emitters.
Idealized perfect sphere, b) spherical cap on cone shaped shank,
parabolic shaped tip, d) tungsten-like specimen with flattened apex.
no shear component of stress because of symmetry. Now imagine the model
of an idealized field emitter (Figure I-3b), a spherical cap superimposed
onto the apex of a cone. One can see that the field and hence the
stresses taper off sharply down the shank where the local radius of
curvature increases. Figures I-3c and I-3d show the added complexity of
determining the electric field distribution and hence the stress
distribution when samples deviate from this ideal model of Figure I-3b.
This leads to significant stress gradients with both tensile and shear
components. The large shear components can lead to massive plastic
deformation and destruction of the specimen (known as flashing).
FIM samples are completely compatible with TEM when the proper
holders are designed and used. In addition when wire samples are used
having a preferred orientation, the crystallography becomes very
simplified. TEM observations of tips are used routinely at many FIM
locations for checking specimen quality.
Two especially designed transmission electron microscope (TEM)
sample holders have been designed and constructed to be used to observe
the influence of the applied field on FIM specimens containing defects.
The first of these two is a "double-tilt" holder used for characterizing
the defects using conventional TEM diffraction contrast. The second is a
"field-effect" holder which is capable of having up to a 5 kV voltage
applied to a FIM specimen in the TEM. The use of these holders is of
considerable importance in understanding how the techniques developed in
this study can be applied to studies of more general types of defects.
These holders facilitate the search for a particular type of defect, and
help to indicate whether it will be feasible to study such defects using
FIM techniques (i.e., is the defect stable under the field-induced
stress?). The TEM has proven to be indispensable with in establishing a
depth scale for specimens analyzed with the IAP.
Microstructure Of Implanted Metals
The microstructure of ion-irradiated metals is dependent on several
variables. These include: ion species, energy, temperature, target
composition, crystallographic orientation, and post-irradiation heat
treatment. The combination of these experimentally controllable
parameters determines the implantation depth, the amount of damage
present in the lattice, the concentration profile, the size and type of
defects, and the precipitation of second phases (if possible). A
complete discussion of these parameters is outside the scope of this
study. The discussion which follows will concentrate only on those
aspects of ion implantation which relate to this study.
The most important parameter which determines the amount of damage
in an irradiated target is the maximum energy, Em, transferred to a
lattice atom in a head on collision with the projectile ion. For
non-relativistic particles, Em is given by
Em = 4Emlm2/(mi+m2)2 1-5
where mi is the ion particle mass, m2 is the lattice atom mass, and E is
the kinetic energy of mi. There are two critical values of Em which
separate implantation studies into three regimes. The first is Ed, which
defines the minimum transferred energy which can produce a stable Frenkel
pair with a probability of i. (A Frenkel pair is a self-interstitial
atom (SIA) and its vacancy.) For values of Em < Ed, no stable damage is
produced. In this regime, the implanted species would be interstitial in
nature (if diffusionally stable). The second critical energy, Ec,
denotes the threshold energy required to form a displacement cascade
(with probability of i) [9-12]. When Em > Ec, the energy is transferred
to a primary knock-on atom that creates the displacement cascade,
characterized by a center depleted zone of high vacancy concentration.
The interstitials are ejected from the zone by either a channeling
process or a focused replacement collision sequence [13,14]. In either
case, the SIA's are found relatively far from the depleted zone.
Seidman and coworkers [14-24] have used the FIM to study depleted
zones in tungsten which are produced by a single incident heavy ion.
They photographically recorded each FIM image after a field evaporation
pulse which removes on the average of one atom from a (222) plane. After
the analysis of numerous frames (on the order of several hundred
thousand), a three dimensional reconstruction of the depleted zone was
accomplished with the aid of the computer. These depleted zones have a
high fraction of clusters (approximately 83%) that are composed of more
than six first-nearest neighbor vacancies, while only about 13% appear as
monovacancies having no first-nearest neighbors . The depth from the
surface of the depleted zones depends on energy and mass. For 20 keV W
into tungsten it is about 20 A . Unfortunately, FIM results on the
structure of depleted zones created by light elements such as hydrogen
and helium have not been achieved to date.
For Ed < Em < Ec, mainly isolated Frenkel pairs are created which
may or may not agglomerate into defect clusters, depending on tempera-
ture, energy,fluence impurity content, etc. For Em just over Ed only
single Frenkel pairs are created. For high dosages, separate-event
interstitials and vacancies can annihilate each other. For increasing
transferred energies, both the number of Frenkel pairs per incident ion
and the clustering of vacancies also increases.
The radiation induced point defects described above will not be able
to be resolved with TEM unless they agglomerate by diffusional processes
with sizes greater than a few nanometers. Here, size refers to either
the physical geometrical size or the extent of the strain field of the
defect. The types of defects which nucleate due to the migration of the
point defects are both vacancy and interstitial dislocation loops, voids,
gas bubbles, etc. In addition, pre-existing lattice imperfections can
trap the point defects and hence change their local contrast. Any type
of lattice inhomogeneity or defect that modifies the local diffraction
conditions will result in contrast in the micrograph. The types of
inhomogeneities which produce contrast include the following:
(1) A locally varying strain field.
(2) A planar defect, e.g., a stacking fault tetrahedron.
(3) A void or gas bubble within the volume observed.
(4) A local change in the extinction length, e.g., due to local
variation in composition.
In general direct interstitial defects are difficult to find,
because they are much more mobile than vacancies at low temperatures. On
the other hand pure vacancy type defects can exist in equilibrium at
relatively high temperatures. The image contrast from small dislocation
loops which are visible in the TEM characteristically have a complex
black-white contrast pattern. The contrast pattern depends on several
factors, material, loop type (vacancy or interstitial), Burgers vector of
the loop, beam direction, extinction distance, and relative position
within the thin foil. The correct identification of small loops from TEM
images therefore requires the aid of computer simulation. The computer
simulation programs use a column approximation to the foil in which the
intensity is found solely by the diffraction conditions within this
volume. The various models used for the calculations for the volumes
containing the defect and strain fields are reviewed by Wilkens  and
Sykes . Sykes et. al  have compiled a catalog of computer
simulated TEM images of small dislocation loops in FCC and BCC metals.
This catalog allows the microscopist to directly compare an experimental
image for a loop with the catalog. The required parameters for the loop
are the depth in the foil, foil thickness, and beam condition. It should
be noted that all the loop contrast patterns are calculated under
dynamical conditions, i.e., "two-beam" conditions. Therefore, all
micrographs compared to simulated images should be made under identical
It must be emphasized that TEM observation of radiation induced
defects is not feasible without an accumulation of the point defects and
the formation of voids and/or loops of sufficient size ( 3 nm).
Thorough discussions of the conditions required to identify such defect
clusters are given by Wilkens , RUhle  Venables and Thomas ,
and Sykes . As mentioned earlier, Seidman and coworkers [14-24] have
used the FIM to study the distribution of clusters in the depleted zone
of a displacement cascade. Their methods can also be used to determine
both types of radiation induced point defects, vacancies and intersti-
tials, and to map their spatial distributions within the emitter. The
FIM is the only microscopic technique which can image point defects at a
temperature at which no recovery occurs. Seidman and coworkers have
utilized the FIM to its fullest in these studies and have contributed
substantially to our present understanding of the spatial arrangement of
point defects in irradiated metals.
Hydrogen In Metals
Most often, the presence of hydrogen in metals is deleterious.
Since metals are frequently exposed to hydrogen, (e.g. containment) the
harmful effects of hydrogen on metals are an important technological
problem. As a result, interest in hydrogen in the field of materials
science extends to both basic and applied research. Because hydrogen has
relatively low-solubilities and extremely high diffusivities in most
engineering alloys the study of the interactions of hydrogen with crystal
defects is of basic importance. The term defect, as used here, means any
microstructural feature differing from a perfect crystalline solid.
Typical defects include: grain boundaries, dislocations, precipitates,
interphase boundaries, vacancies, etc. The analysis of hydrogen
associated with these defects cannot be studied by conventional electron
probe techniques, such as analytical electron microscopy (AEM), energy
dispersive x-ray spectroscopy (EDXS), electron energy loss spectroscopy
(EELS), scanning electron microscopy (SEM), and Auger electron
spectroscopy (AES), because these techniques are incapable of detecting
it. Surface analytic techniques employing mass spectrometers for
example, secondary ion mass spectrometry (SIMS) can detect hydrogen, but
so far lack sufficient spatial resolutions. This spatial resolution
includes both the lateral probe diameter and depth profiling resolution.
The quantity of hydrogen which can cause harmful effects to alloys
can be extremely small and hydrogen defect interactions can be on
extremely fine scale. Thus the techniques which can analyze hydrogen
must have high sensitivity for it and adequate spatial resolution in
order to study the mechanisms of degradation.
It has long been known that field ion techniques are extremely
sensitive to the presence of hydrogen. In fact, this sensitivity has
made it difficult to apply FIM and atom probe techniques to studies of
hydrogen. In general all hydrogen studies using the FIM must overcome
the same problems: 1) hydrogen's high diffusivity, even at low
temperatures, 2) the apparently low solubility of hydrogen in the absence
of defects, and 3) hydrogen is ever-present in the experimental
background. Experimentally this means that hydrogen must be introduced
into the metal, kept there for sufficiently long time to be analyzed, and
confidently distinguished from pervasive background hydrogen.
Background hydrogen is always a consideration in mass spectrometric
techniques because it is a major constituent in all normal vacuum
systems, since it is difficult to pump. With FIM techniques the
background hydrogen problem is further aggravated by the phenomenon of
field adsorption. Field adsorption occurs because of the polarization of
the hydrogen gas molecule under the influence of the applied field on the
emitter. The rate of adsorption in the presence of a field and at a
given partial pressure of hydrogen is several orders of magnitude higher
than without the applied field. The consequence of this is that a
hydrogen background desorption peak is present in all atom probe studies.
To circumvent this problem, deuterium is used in this study instead of
hydrogen. The deuterium and hydrogen signals are well differentiated in
The introduction of hydrogen ex situ (with respect to the FIM/IAP
chamber) requires very complex quenching and cryogenic/UHV transfer
techniques. This difficulty is in addition to the elaborate control
experiments required to determine the adsorption of hydrogen in all the
steps preceding introduction into the FIM/IAP chamber. For these reasons
in situ implantation of deuterium was chosen for the present study. This
method offers major advantages since 1) both the deuterium and the
defects can be reproducibly and controllably introduced into the lattice,
2) the background deuterium can be controlled by differential pumping and
valving, 3) the number and complexity of the control experiments can be
greatly reduced, and 4) the deuterium can be easily distinguished from
the hydrogen background.
There are major questions which must be answered before the FIM/IAP
can be applied to studies of general types of defects (i.e., those not
induced by ion implantation). These questions will be addressed and
answered in this study. The most important of these will be the
feasibility of implementing a differentially-pumped ion gun for in situ
implantation with respect to the deuterium field adsorption. Any ion gun
coupled to the FIM/IAP and used for ion implantation of deuterium will
contribute a deuterium partial pressure to the FIM/IAP chamber. The
question arises, can the deuterium partial pressure be kept sufficiently
low so as not to interfere with the implanted deuterium as detected with
an IAP? This study will show that this question can be answered in the
affirmative when special precautions are taken.
A major impetus for studying hydrogen in metals is the phenomenon of
hydrogen embrittlement in commercial alloys, especially steels. Because
of hydrogen's extremely high diffusivity, even at low temperatures,
failures involving hydrogen embrittled alloys usually occur catastrophi-
cally. Unfortunately, the mechanisms of hydrogen embrittlement are still
little understood. In steel at least five different mechanisms for
hydrogen embrittlement have been proposed. For example, Zapffe and Sims
 developed a pressure-expansion theory in which very large gas
pressures within internal micro-cracks and voids cause either plastic
deformation or cleavage. This leads to a coalescence of the micro-voids
and to eventual failure. However, this mechanism is inadequate to
explain hydrogen embrittlement which occurs with hydrogen gas pressure of
one atmosphere or less. Another proposed mechanism, by Petch and Stables
[30,31], suggests that hydrogen adsorption lowers the energy of the
surface created in crack propagation, which in turn lowers the work of
fracture, according to Griffith's criterion. There are several
criticisms of this mechanism as well [32-34] and it seems not to be
The decohesion theory proposes that high concentrations of hydrogen
lower the intrinsic cohesive force between atoms [35,36-38]. It is
postulated that the stresses developed at crack tips promote the
accumulation of hydrogen to very high concentrations and thus substan-
tially lower the cohesive forces. Unfortunately, the dependence of the
maximum cohesive force on hydrogen concentration, interface structure,
and alloy composition is not known. Still another theory proposed by
Westlake  also centers on the processes occurring near a crack tip.
It is postulated that hydrogen concentrates near the tips of cracks
because of the hydrostatic stresses present there. A high enough hydrogen
concentration, in turn, leads to hydride formation. Embrittlement then
is thought to occur due to hydride cracking near the crack tip. In fact,
Gahr et al. have shown that the hydrostatic stress field of a crack tip
can stabilize hydrides in niobium which are otherwise unstable .
They also demonstrated embrittlement due to hydride cracking. For iron
and steel, no hydride is stable up to 2 GPa  and Westlake's model is
not considered applicable [32-42]. Nonetheless, calculations of the
hydrogen atmosphere at a crack tip show that very high concentrations can
occur there and that the hydride formation model could be appropriate
Trapping Of Deuterium
Kellogg and Panitz  have directly observed the trapping of
deuterium at a grain boundary in tungsten. In this study seven tungsten
emitters were implanted with low energy (200 ev) deuterium ions. The
specimens were imaged with the TEM and then transferred to a FIM/IAP and
analyzed. The FIM/IAP can give a time gated image which can map the
distribution of deuterium with depth. (The FIM/IAP and its modes of
operation will be discussed further in Chapter II.) The only sample that
retained any deuterium was one in which a grain boundary was present, the
gated IAP image showing the deuterium associated with the grain boundary
visible in the FIM micrograph. In a more recent set of atom probe
experiments, Macrander and Seidman  have shown that 200 eV H; ions
implanted into Tungsten emitters completely diffuse out of the samples at
a temperature of 290K. Their results indicate a diffusion coefficient at
290K that is greater than 10-17 cm2/sec. Since the implanted specimens
in Kellogg's and Panitz's study were stored at room temperature for
several days and were heated during imaging somewhat in the TEM, grain
boundaries are apparently deep traps for deuterium.
In the second study, Panitz  demonstrated the importance of
using control experiments to distinguish the difference between the
implanted and the background deuterium signal in the IAP spectrum.
Implantation was done in the specimen pre-chamber of the IAP and not
in situ. Complex control experiments were required because the
implantation was performed outside the IAP chamber. This suggests the
possible benefits which could be derived if in situ implantation were
The results of Panitz's study indicate that the 80 eV ions are
implanted to a depth of 49 A at 3000K and that adsorbed surface species
selectively scatter some of the deuterium into preferred channels. These
results are at odds with those of Macrander and Seidman  which
indicate that the deuterium should have diffused out of the sample since
no implantation damage can occur with 80 eV deuterium ions implanted into
tungsten. The implantation was carried out at 3000K where the solubility
of hydrogen is extremely small and the diffusivity is high. With these
considerations the implanted deuterium should have diffused to the
surface where it would have been field desorbed. A possible explanation
for the discrepancy is that the background deuterium has not been
accounted for adequately. There is the possibility of surface migration
of deuterium up the shank during the profiling experiment. This
deuterium would appear in the IAP spectra as an implanted ion. A change
in evaporation rate due to a voltage increase during the analysis can
change the arrival rate of the deuterium to the analyzed portion of the
tip. Another factor which could affect a possible background signal is
the time interval between field desorption pulses. These factors were
not reported in this study .
Hren  confirmed the necessity for in situ studies when he
performed several ex situ experiments preliminary to this dissertation
using the facilities of Myers* and Panitz and Kellogg A discussion of
the design requirements for coupling an ion gun to a FIM/IAP will be
presented in Chapter II. The control experiments associated with in situ
implantation of deuterium are relatively simpler than for ex situ
implantation and will be presented in Chapter III.
Nitrogen Implantation In Metals
Nitrogen is by far the most widely used element for the modification
of the surface properties of alloys to improve their wear resistance.
*Ion Implantation Facility, Sandia National Laboratories,
**Surface Physics Division, Sandia National Laboratories,
There is a great deal of research being done in the area of determining
the mechanisms for the improvement of wear resistance in a variety of
alloy systems. It should be noted that not only the wear characteristics
are improved by implantation, but also often are such properties as
fatigue, corrosion (both atmospheric and aqueous), toughness, strength,
and high temperature oxidation. Wear resistance, however, is the common
goal of applying ion implantation to alloy systems. Wear can be improved
by increasing the surface hardness, by reducing the friction coefficient,
by modifying the subsurface composition and structure to resist fracture
and debris formation, and/or by increasing the wetability of the surface
to lubricants. This lack of understanding of the basic mechanisms of
wear improvement has not stopped the spread of industrial applications of
ion implantation of nitrogen. The major thrust of commercial use of
implantation involves tool steels and Co-cemented WC [49-52]. The area in
which ion implantation is very attractive is where little or no
dimensional changes and low processing temperatures are desired. It is
also of interest where delamination of coatings applied by more
conventional techniques may be a problem . Basic research efforts
are directed towards understanding the wear reduction mechanisms in
technologically important alloy systems such as stainless steels [53-55],
hard chromium plate , Ti-6AI-4V [57-60], and Co-cemented WC [61-63].
The increases in wear resistance are usually attributed to nitride
formation and/or Cottrell atmosphere hardening. The nitride formation by
implantation is usually in the form of finely dispersed, hard
second-phase precipitates. The Cottrell atmospheres arise from nitrogen
being attracted to dislocations and pinning them preventing them from
being mobile and thus hardening the material. Depending on the material,
one of these may be more predominant than the other. For example, mild
steels without alloying elements having strong affinities for nitrogen
such as Al, Cr, Mo, V, and Ti do not show dramatic increases in wear
resistance upon nitrogen implantation . One disadvantage to nitrogen
implantation to improve the wear characteristics of an alloy is that the
benefits are not retained at elevated temperatures. High operating
temperatures must be avoided and this sometimes precludes its use in
particular applications such as tools for chip forming. This is thought
to be due to the instability of nitrogen-defect structures which are
responsible for the improved wear characteristics [51,62]. This is
supported by experiment. For example, Dose Santos et al. have seen
nitride and carbo-nitride formation upon implantation and then subsequent
dissolution at higher temperatures .
The understanding of the wear mechanisms are complicated by studies
in which the nitrogen is seen to still be retained beyond the original
implantation depth. The depths that the nitrogen is still modifying the
surface behavior can be 10-50 times the implanted range . Clearly
this nitrogen retention is happening during the wearing of the material
and microstructural changes must be occurring. There are several
proposed ways for this to happen. During wear, the rubbing of asperities
on the two surfaces causes localized heating. This thermal heating is
thought to be responsible for the dissolution of the nitride phases and
diffusion down the steep temperature gradient . This mechanism would
agree with the observations that nitrogen implantation does not give good
results at high service temperatures. These local temperatures may be as
high as 10000K (e.g. Fe2N has been shown to be stable in the electron
microscope to 9000K ). This same local heating could also cause, the
nitrogen, decorating dislocations to diffuse deeper into the material
. Another possibility for the retention of nitrogen is the
continuous transfer of nitrogen back and forth between the surfaces as
the wear front advances .
Ion Beam Carburization
Several investigators have reported improvements in properties in
alloy systems with the implantation of inert elements such as neon, argon
, and zirconium . Others report that no effects are seen when
elevated temperatures (500-6000C) are used during implantation . The
probable explanation of this is due to beam carburization of residual
hydrocarbons in the vacuum system decomposing under the effects of the
irradiation during implantation. Elements with high affinities for
carbon tend to form carbides giving a characteristic improvement in
surface hardness. It is more likely that at high temperatures the
decomposed hydrocarbons are not stable and reform rather than the carbide
phases being unstable. The resulting carbide phases would necessarily be
quite small and finely dispersed.
Applicability Of FIM Techniques To Nitrogen In Metals
A variety of techniques have been applied to study the composition
and morphology of implanted surfaces. These include secondary ion mass
spectroscopy (SIMS), Auger electron Spectroscopy (AES), scanning electron
microscopy (SEM) with energy dispersive analysis of X-rays (EDAX),
Rutherford backscattering (RBS), nuclear reaction analysis (NRA), and TEM
(and analytical electron microscopy, AEM). With the exception of TEM,
all of these techniques have the ability to use the same samples which
are used for the wear tests. Several of them can also analyze small
particles within the wear tracks of the samples.
Field ion microscopy techniques offer some appealing features for
studying nitrogen (and other elements) implanted into metals. It is a
surface microscopic technique and the results can be directly compared
with that of some of the above technique. It has the capability of
resolving both the defect structure caused by implantation on an atomic
scale and small precipitate phases which form. It has the ability to
dissect these features as a function of depth with an accuracy of
d-spacing of the material. The same method for determining the depth
scale can be used with atom probe analysis, both AP and IAP, to give
chemical information as a function of depth. Because the FIM samples are
completely compatible with the TEM, the implanted samples do not require
any further sample preparation to observe them there. In other words,
the implanted structure is accessible to two high resolution microscopic
and analytical techniques with no treatment to them after they have been
implanted other than to introduce them into the specific instrument.
The delicate nature of a FIM specimen in terms of its geometry
precludes it from also being used in wear test apparatus. However, the
relationship between the microstructure and macroscopic properties of
materials is one of the principal goals in materials science. The FIM
sample lends itself to investigation by two microscopic techniques, FIM
and TEM, without further specimen preparation after implantation. This
study of the implantation depth of implanted nitrogen into tungsten and
nickel in is the first step in applying the FIM/IAP to the future use in
using it to observe and analyze the small nitride, carbides, and
carbo-nitrides responsible for wear reductions in many ion-implanted
samples. These types of precipitates in emitters have proven to be very
amenable to FIM and AP analyses in the past.
The instrumentation employed in the experimental work can be divided
into three categories: FIM/IAP, ion gun, and transmission electron
microscope. This chapter will describe the unique features or techniques
which have been developed in utilizing these instruments for the present
study, as well as document the instrumentation.
Field Ion Microscope/Imaging Atom Probe (FIM/IAP)
Until recently, no commercial FIM/IAP has been available and each
instrument has been custom-built and usually designed with a specific
purpose in mind. The FIM/IAP used in this study is no exception, and
several unique features have been incorporated in it which will be
discussed. It was designed to be a versatile instrument for metallur-
gical applications. The electronics and timing circuitries are based
primarily on those of Panitz . The vacuum chamber, specimen exchange
mechanism, specimen holder/manipulator, and chevron/phosphor screen
assembly have been designed primarily by this author. The construction
of the FIM/IAP proceeded in stages. Each was a major design or
developmental stage in the instrument leading to its present form. Most
of the problems associated with each of these stages have been solved by
this author. Several features have been included because of considera-
tions to the present study or anticipated future studies involving
hydrogen. Many of the design features or specifications within each
stage are either common to both or intimately related. Figure II-1 is a
diagram showing these major stages and the relationships between them.
The arrows in this diagram indicate these relationships. A double-headed
arrow represents the fact that the one stage is intimately related to the
other and must be compatible. A single-headed arrow represents an
independence, but that some of the same requirements in the one stage are
also requirements in the other. The details of the design and
interactions of the various stages represented in Figure II-1 will be
described in each of the following sections. This chapter will provide
the bulk of the documentation required for someone to learn to use this
The FIM/IAP used in this study differs from other instruments in
that the sample can be directed towards two, six-inch ports separated by
1500 (Figure II-2). One of the six-inch ports is used as the FIM/IAP.
It has a chevron assembly  mounted 15 cm from the chamber's axis.
The assembly uses flat microchannel plates from Galileo Electro-Optics
and was designed by this author. The other port is a utility port.
Various options are available for use with this port which provides the
versatility of this instrument. Originally, a conventional atom-probe
 was planned to be attached to it after completion of the IAP. For
the present study a Colutron Research Corp., model G-2-D ion gun was
coupled to this port (Figure 11-3). This gun was obtained as a kit, and
Figure II-1 Block representation of the major development stages of the
FIM/IAP. The double-headed arrows indicate sections whose parts or
design requirements must be compatible. The single-headed arrows
indicate stages with sections having similar requirements as to those of
the section of the arrow's origin.
Figure 11-2 View of the FIM/IAP shown from the IAP side. To the right
is the associated electronics. The ion gun can be seen in the
Colutron ion gun coupled to the HFM/IAP.
then assembled, tested and made operational by the author. This port has
also been used as a conventional FIM with a 7 cm tip-to-screen distance.
Other uses for this port are anticipated, including an evaporation source
and an electron gun for heating the sample.
Midway between the two ports described above is a mini-flange port
(1.33 in. 0.0.) used for the exchange of the specimen. Figure 11-4 is a
photograph of the exchange chamber. Huntington Mechanical Laboratories
supplied the major hardware for the exchange system, including an MS-075
straight-through valve, a VF-169-10 magnetically-coupled linear/rotary
drive, the special 6-way cross, and special 1.33 to 2.75 in., 0.D.
nipple. The minimum inner diameter is .625 in. which is that of the
valve. A positioning device coupled to a bellows is used to align the
insertion rod with the sample stage in the main chamber. A viton gasket
is used for the blank flange used for the specimen exchange. A special
clamp is used in lieu of bolts to seal this flange. A 170 1/s Balzers
turbo-pump used on the ion gun is also shared with the exchange
mechanism. An all-metal, bakeable valve separates the two volumes. An
absorption pump first roughs the exchange valve to approximately 1x10-3
Torr. The valve is opened very slowly to the turbo-pump and an ultimate
pressure of about 1x10-6 Torr is achieved in approximately 10 minutes.
The chamber is roughed by two absorption pumps used in series. A
pressure of about 2x10"- Torr can be achieved with these. A Perkin-Elmer
80 1/s ion pump is used as the primary pump to attain UHV pressures.
This pump has special elements for higher pumping speeds for hydrogen.
It is assisted by a Perkin-Elmer, liquid nitrogen cooled titanium
sublimation pump. Additional pumping arises from the Air Products
Figure 11-4 Close-up photograph of the FIM/IAP showing the introduction
of a sample into the chamber using the Huntington rotary-linear,
magnetically coupled feedthrough.
Displex helium closed cycle refrigerator used for cooling the sample. A
pressure of about 1x10-9 Torr can be achieved with the ion/Ti sublimation
pump combination. The cryopumping usually brings the system pressure to
about 5x10-10 Torr.
Although all the components in the vacuum chamber are bakeable to at
least 300C, this system has not been baked to achieve ultimate vacuum
conditions. The system is, however, subjected to a procedure which does
lower the pressure considerably. The conductance between the ion gun and
FIM/IAP is approximately .01 1/s. Dry nitrogen from liquid nitrogen in a
dewar flask is bled into the system through a leak valve. The valve
between the ion gun and the main chamber is opened. The heater on the
ion pump is turned on. By properly adjusting the leak valve, a pressure
of about 1x10-1 Torr in the chamber and 9x10-4 Torr in the ion gun is
achieved. These conditions lead to an intermediate flow regime for the
nitrogen which helps drag difficult-to-pump gases such as He, Ne, and
water vapor out of the main chamber. This is done for eight hours, after
which the system is pumped down to 1x10-5 Torr by the turbo-pump, the
valve closed, and the ion pumps started.
An imaging gas, either He or Ne, is admitted into the system by leak
valves after the ion pump is turned off. The gas lines from the
cylinders are carefully baked out when cylinders are changed. When He is
admitted into the chamber, the pressure is monitored carefully until the
desired pressure is achieved. The valve is immediately turned off.
Helium is not pumped effectively by the cryopumping of the Displex
refrigerator and the pressure is stable. The Ne is, however, pumped by
this system and the valve must be opened very carefully to a set point to
maintain a stable pressure. It was found that this set point is more
easily achieved if the valve in the beam line to the ion gun is opened
and a steady state condition is found. Furthermore, it was found that if
the Ne leak valve is turned off, the turbo-pump will pump the main
chamber to approximately 1x10'6 Torr. Closing the valve to the ion gun
and turning the ion pump on achieves a lower ultimate pressure than if
the ion pumps were used alone from the imaging pressure.
There are extreme requirements imposed on the design of the FIM/IAP
specimen stage. For a relatively simple holder with no manipulation,
there are three major and somewhat conflicting requirements: i) the
sample must be cooled to cryogenic temperatures, ii) a high voltage of up
to 15 to 20 kV must be applied to the sample and iii) all materials must
be UHV compatible, which includes being bakeable to at least 3000C. For
good thermal conduction, OFHC copper is used. For poor thermal
conduction, 304 stainless steel with a thin cross-sectional area is used.
For electrical insulation with good thermal conduction, two materials can
be used, either boron nitride or sapphire. Because sapphire is extremely
difficult to machine, boron nitride was utilized for all holders designed
for this instrument.
For metallurgical applications using the FIM/IAP, manipulation is
also required further complicating the design. Two orthogonal tilt axes
located at the specimen's apex allow the specimen to be examined thus,
the disadvantages of the limited viewing area due to the increased
tip-to-screen distance are overcome. This helps in crystallographic
indexing of the sample and orienting a particular feature of interest for
analysis. Linear motion in the X, Y, and Z directions is needed for
alignment with the exchange rod and also with the ion gun. The two
six-inch ports in the chamber, separated by 1500, add another complica-
tion in that both ports have the same degree of motion associated with
them. A design requirement for this instrument was that the specimen
should have a maximum of 300 in the extreme rotation position for each
port, thus giving a total of a 2100 rotation angle that the holder
Figure 11-5 shows a photograph of the specimen stage and manipu-
lator. The stage consists of a cylindrical outer conductor of copper and
stainless steel. The stainless part is attached to the manipulator so
that the vertical rotation axis is in-line with the specimen. This
connection also serves as the fulcrum for the up/down tilt supplied by a
rod at the end of the cylinder. Copper braid (Beldon wire 5558) is
silver-soldered to a collar on the copper portion of the outer cylinder.
The other end of this braid is silver-soldered to a copper block (button)
which is fastened to the end of the Displex refrigerator with a bolt.
The silver-soldering of this braid proved to be the weak stage in this
design. An improved braid/cold finger arrangement is described in
Appendix A. There is an inner concentric copper rod into which a copper
sample holder is screwed. This inner copper piece is held in place by
two boron nitride insulators and tightening a copper nut on the threads
of it. The boron nitride insulators are machined so that a high voltage
breakdown path is not straight across the face of the insulator but is
blocked by concentric ribs in them. When the system is cooled, the parts
are contracted, making the fit even tighter. Since the heat path is from
Figure 11-5 Manipulator/Sample holder, a) is a photograph of the
manipulator and sample holder outside of the FIM/IAP. Cooling braid is
not attached. b) shows the holder in situ through one of the six-inch
the sample, through the boron nitride, through the outer cylinder,
through the braid, the outer cylinder will be colder than the specimen,
providing some cryopumping directly around the tip. The stainless steel
in the outer cylinder proved not to be the best design. An improved
design (Appendix A) has an all copper outer cylinder. There is no
radiation shield for this holder but one has been incorporated in the
The hardware attaching the manipulator to the cylinder provides the
motion and the thermal insulation from room temperature. The vertical
cylinder in Figure 11-5 is 304 stainless steel. There is a .010 in.
thick thin-walled section in this piece. This thin wall and the length
of the prongs going down to the pivot points provides most of the poor
thermal conduction. This section has been improved upon in the new
design (Appendix A). The up/down tilt is provided by the coaxial-linear
drive in the rotary feedthrough of the Huntington manipulator being
coupled by a rod to the outer cylinder. The length of travel in this
drive is approximately .5 in. At room temperature this provides about
300 to the sample holder. At cryogenic temperatures, the increased
stiffness of the copper braid resists the relaxation of a spring inside
this manipulator and thus limits the upward motion of the specimen stage.
A stiffer spring was tried but with little success.
The high voltage leads to the sample come down through this
stainless steel cylinder. A thin-walled stainless steel tube is
insulated with a glass tube and goes through a 2100 crescent hole cut in
the connecting flange between the large vertical cylinder and smaller
diameter rod. A flexible, stainless steel, catheter guide connects this
lead to a stainless steel pin screwed into the inner conductor for the
sample stage. This electrical path is well insulated both electrically
and thermally and is mechanically stable.
The following are the operating characteristics of this holder. The
ultimate temperature is 650K. The breakdown voltage of this stage is in
excess of 20 kV. During operation breakdown first occurs in the external
connection of the high voltage lines. A full 2100 rotation is available
which includes the 30 at the extreme positions. About +50 to -350 is
available from second tilt axis. A new sample introduced through the
sample exchange port is cooled within 30 min. Sufficient manipulation of
the XYZ and tilt on the Huntington manipulator is present to center the
sample in the beam of the ion gun. The alignment procedure for the ion
gun with the sample holder is described in Appendix B.
A field-limiting aperture  is conspicuously absent from this
specimen stage. Eaton and Gibson  have shown through finite-
element calculations that the electric fields decrease rapidly away from
the tip. In atom probes employing a field-limiting aperture, the
mass-to-charge ration, m/n, is found by using the equation,
m/n = 1930-(Vdc +a*Vp)t2/D2 II-1
where Vdc is the applied d.c. voltage in kV, Vp is the pulser charging
voltage in kV, a is the fraction of this voltage which reaches the tip, D
is the tip-to-screen distance in m, and t is the time-of-flight in
microseconds . Masses found with this equation and also by taking
the ratios of the squares of a known and unknown mass agree quite well.
General Description Of The IAP
The physical appearance of an IAP is very similar to that of a
simple FIM. The most obvious differences are the longer tip-to-screen
distance and the increased number of cables and instrumentation attached
to the electron multiplier channel plate/phosphor screen combination.
The IAP's flight distance is usually between 10 and 45 cm. The channel
plates, instead of a single plate, are incorporated into a chevron
configuration, and have a maximum gain of approximately 1x107 The IAP is
a time-of-flight mass spectrometer with two operating modes. Ionization
of the surface is initiated by high voltage pulses superimposed on the
applied d.c. voltage to induce field evaporation. The detector of the
system is the chevron assembly (including phosphor screen), which also
serves as the imaging screen for the instrument in the FIM mode, but is
operated at full gain. In the TOF mode, the instrument is essentially an
atom probe with a very short flight distance and very large defining
aperture. All atoms viewed in the FIM image will strike the detector in
the IAP's TOF mode. The spectra obtained from the IAP are recorded with
very fast storage scopes or transient waveform digitizers. The
time-of-flight of the field evaporated ions are dependent on their
specific mass-to-charge ratio, m/n, by equation II-1. The analysis of
the TOF spectra is, therefore, straightforward. It should be noted that
the mass resolution is extremely poor, approximately 20 to 50, because of
the short flight distance.
The time-gated mode of the IAP is used to form an image using a
selected mass in the TOF spectrum. The image formed is caused by the
actual atoms from the tip striking the detector. These ions are selected
by "switching on" the detector to coincide with the arrival time, and
then the detector is "switched off" again. Only those ions arriving
within this time window will result in an image. The gating on and off
of the detector is accomplished by putting a high voltage pulse (formed
in the same manner as the desorption pulse, except the high voltage
switch employs a Krytron tube) onto the chevron assembly. The time
window's duration is determined by the pulse width, which is determined
by the charging cable length. In the instrument used in this study, the
pulse width is 50 nsec. The selection of the particular mass is
accomplished by delaying the triggering of this pulse to coincide with
displayed TOF peak. Usually, several pulses are integrated into one
micrograph by putting the camera in the "bulb" mode. The resulting
micrographs, when compared with the FIM image, are capable of displaying
with the same spatial resolution very sharp concentration gradients
across interphase boundaries, and grain boundaries .
The heart of the IAP is the Tektronix 7912AD transient waveform
digitizer. It is extremely fast and has a digitizing rate of up to 100
GHz. The 7912AD is used primarily for collecting time-of-flight (TOF)
data and setting up the proper conditions for the time-gated imaging
mode. It also proved to be indispensable in determining cable and
instrumental delays as well as system characteristics such as pulse
shapes. The 7912AD can be operated in a limited way from the front
panel, but is designed for operation via the General Purpose Interface
Bus (GPIB or equivalently IEEE-488 interface). An important feature of
the digitizer is that several waveforms can be added internally in a
"signal average" mode. Three benefits are derived from this: i) the
signal to noise ratio is improved, ii) collection of data can proceed at
a much higher rate, and iii) the demand for computer storage of the
waveforms is relaxed.
Figure 11-6 is a block diagram of the electronics and computer
system of the IAP in the TOF mode. All cables are terminated with 50 0
impedances. There are two pulse pickoffs on the desorption pulse line.
A Tektronix model CT-3 is the first in line on the desorption pulse line.
It triggers the digitizer to sweep. The second pickoff is located just
before the pulse line enters the vacuum system. The design of this
pickoff was suggested by Miller*. It serves two purposes: i) it
terminates the pulse with a 50 0 impedance and ii) it picks off the pulse
signal reduced by a factor of 21 to send to channel 1 of the digitizer.
The coaxial cable leading from this pickoff to the digitizer is the same
length as the one leading from the chevron plate detector to channel 2 on
the digitizer. When the two channels are summed, the flight time is
exactly that between the displayed pulse and the particular
mass-to-charge species because all time delays due to cables have been
considered. It should be noted that the time for conversion from the
incident ion to the output in the chevron assembly is considered
Figure 11-7 shows an analyzed spectrum from an Fe-Mo-N system
previously studied by this author . Several features of the spectrum
should be discussed. The spectrum is the result of having the digitizer
"signal-average" 16 waveforms. The lower left corner gives the d.c.
Miller, M. K., private communication.
I. E-3 V FeMoN 84022813 *0
KVDC=12.22 KVP=4.44 16 Pulses TFILE* 26
Figure 11-7 Analyzed spectrum of an Fe-3at% Mo specimen which has been
internally nitrided. The field evaporation voltage was 13.99 kV
(12.22 d.c. + 0.4 x 4.44 pulse) at a temperature of 650K.
voltage of 12.22 kV and the pulse charging voltage of 4.44 kV. With the
pulse voltage being 40% of the charging voltage, the voltage for field
evaporation was 13.99 kV. The time base of the digitizer was .1 sec/div,
giving 1 sec full scale. The vertical amplifier was set at 5 mV/div,
indicated by the step between solid vertical lines multiplied by the
scale factor, 1x10-3 V. Note that the seven naturally occurring isotopes
of Mo (A=92, 14.8% relative abundance; 94, 9.1%; 95, 15.9%; 96, 16.7%;
97, 9.5%; 98, 24.4%; and 100, 9.6%) are not resolved but their presence
is reflected in the widths of the peaks. The two peaks indicated with
the "*" are due to the combination of a ringing in the detector induced
by the high voltage pulse and the truncation of the negative-going part
of the ringing when the digitizer was used on the 5 mV scale. This
condition has been remedied since this system has been studied and no
longer interferes with the analysis of spectra.
The timing considerations for the time-gated mode of operation are
rather more involved than the TOF mode. Figure 11-8 is a block diagram
of the IAP in the time-gated mode. In this mode all delays must be
determined precisely. Once all the possible delays in the instrument are
accounted for, the operation of the IAP in the time-gated mode is
straightforward. To set it up in this mode, the cable from the CEMA
output to channel 2 of the digitizer is disconnected and the voltage on
the second plate is reduced to 1 kV. Since the voltage across this plate
is zero, the gain of the chevron assembly is also zero. A Minolta XG-7
SLR 35 mm camera using Kodak 2475 Recording film is opened in the "Bulb"
mode. The number of pulses for the integrated photograph is set on the
(A) TOF Mode
(1) Pulser fires. 1st pickoff pulse goes to trigger scope.
(2) 1st pickoff triggers scope. (delayed sweep with second time
(3) HV Pulse arrives at tip. 2nd pickoff pulse sent to channel 1
(4) 2nd pickoff pulse displayed on scope.
(5) Ionic mass species strike detector.
(6) Mass signals inverted and displayed on scope.
(B) Time-Gated Mode
H(2) (3) 1I
I n n I I I k \
(1) Pulser fires. 1st pickoff goes to delay generator
and to trigger scope.
(2) Pickoff pulse triggers delay generator and scope.
(3) Delay generator sends delayed pulse to gate pulser.
(4) HV pulse arrives at tip. 2nd pickoff pulse sent to scope.
(5) 2nd pickoff pulse displayed on scope.
(6) Gate HV pulse arrives at channel plates coinciding with the
arrival of mass species. A gate pickoff was sent to "Z-in" on
scope when gate pulser fired and is not shown for clarity.
(7) Trace on scope is intensified, outlining the portion of
spectrum in which plates are active.
Figure 11-9 Synchronization diagrams of the IAP in a) TOF mode and b)
in time-gated mode. The larger pulses correspond to high voltage pulses,
small pulses to 5v logic pulses, and exponentially decaying pulses to
real and displayed signals.
control panel of the desorption pulser. The sequence of events for
gating the channel plate is initiated by each desorption pulse. Figure
11-9 shows the timing sequence and the instrumental and intentional
compensating delays which occur in the IAP. Comparison of this sequence
with Figure 11-8 and the description which follows will help the reader
follow what occurs during the operation in the time-gated mode. When the
mercury-wetted reed switch of the desorption pulser fires, the pulse is
sensed by a signal pick-off immediately. The high voltage pulse is
intentionally delayed by a 53.2 m cable (Figure 11-8, label G) to
compensate for instrumental delays.
The pick-off pulse goes to the Berkeley Nucleonics Corp. Model 7050
digital delay generator through cable (B). The delay generator (C)
supplies two pulses, an initial pulse and a delayed pulse. The initial
pulse output triggers the digitizer trace through cable (J). The delayed
pulse triggers the gate pulser through cable (D). The gate pulse is sent
through cable (F) to the second channel plate in the chevron assembly.
The channel plate is turned on for 50 nsec, the duration of the pulse.
This cable is carefully terminated into 50 0. The delay generator is set
to the time-of-flight of the desired mass specie. A cable (I) from the
gate pick-off to the "Z"-intensification on the digitizer enables the
mass to be visually selected. The delay generator is changed until the
intensified portion of the trace overlaps the mass peak's position. The
shutter of the camera is closed when the pulser stops.
Computer And IEEE-488 Instrumentation
The computer coupled to the IAP is a Tektronix model 4052A desktop
computer. It uses an extended form of the BASIC programming language,
especially designed for graphics and instrumentation control over the
IEEE-488 interface bus. This is called the General Purpose Interface Bus
(GPIB) by Tektronix. There are four instruments on the GPIB: i)
Tektronix 7912AD transient waveform digitizer, ii) Scientific Instruments
5500 temperature indicator/controller, iii) Bertan 205A-30R D.C. high
voltage supply, and iv) Tektronix 4662 Interactive digital plotter. The
7912AD and the SI 5500 are both microprocessor controlled and can operate
independently of the 4052A, thus freeing the computer for other
A Tektronix 4909 File Manager system is also on the GPIB. The 4909
is a hard disk storage drive with a total of 96 Mbytes of memory.
Although it is on the GPIB, the interface is transparent to the user
because it has no address and is controlled through a ROM pack inserted
into the 4052A. The 4909 has been proven to be indispensable when the
large number of waveforms in a depth profile are collected. During
profiling, each waveform is stored while the digitizer is collecting the
next waveform. This procedure minimizes the dead time between the
collection of waveforms. Minimal data reduction is done to further
increase this efficiency. Additional storage is provided by magnetic
tape cartridges for the 4052A and an internal 256 Kbytes extended file
manager. With the extended file manager is also a serial communications
interface. There are four ROM slot positions. The third position must
contain the 4052R10 advanced file manager ROM pack for the 4909. Two ROM
packs are required for the operation of the IAP. The first is a TransEra
732-BCD I/0 ROM pack. It has 40 lines, 32 of which are configured by
software to be either input or output for binary coded decimal (BCD)
information. Four digits each from the meters of the high voltage supply
and the pulser's charging supply are read by the computer over these
lines. Each of these meters has 4-1/2 digits. Since each meter has only
16 lines, the least significant digit is disregarded. This ROM pack has
four control lines and four status lines, the latter not being utilized.
Two control lines are used to start and stop the pulse control unit.
The second ROM pack required by the IAP control software is the
Tektronix 4052R07. This ROM pack facilitates the handling of dimensioned
arrays. Waveforms from the 7912AD are 512 point arrays. The ROM pack
programs include MIN, MAX, CROSS, INT, DIF2, DIF3, and DISP. The MIN,
MAX, and CROSS commands find the indices of the minimum, maximum, and
where the waveform crosses a particular value. The INT command performs
a numerical integration of the array while the DIF2 and DIF3 commands
perform a two or three point numerical differentiation. The DISP
displays the complete waveform on the 4052A's screen very fast.
The Tektronix 7912AD is the fastest digitizer which exists. It can
capture a single trace within a 5 nsec window into a 512 point array with
full 9-bit resolution. It utilizes Tektronix 7000 series plug-in
modules. The plug-in modules used in the IAP are the 7A24 dual time base
and the 7B28 dual channel amplifier. The dual time base was chosen
because a portion of the waveform can be expanded. The dual channel
amplifier allows the pulse pickoff to be displayed in addition to the
output from the chevron assembly. The 7912AD can be operated in a
limited fashion from the front panel. In the non-storage or TV mode, the
waveform is displayed on a monitor in real time. The monitor is used to
set the beam intensity and to set the proper operating conditions such as
time base and amplifier settings. When the digitizer is used from the
front panel in the digitize mode, a dual parallel trace is displayed on a
Tektronix 2213 oscilloscope. It is important to understand how the
digitizer works and why the dual trace occurs because of the importance
of setting the beam intensity properly. There are two electron beams in
the digitizer, a "writing" and "reading" which face each other. The
"reading" beam charges a solid state array chip and is scanned vertically
from left to right. The "writing" beam discharges part of the array.
When the slower reading beam scans these areas again, a current is sensed
indicating the results of the writing beam. The two traces displayed are
two arrays where the reading beam senses the change of state from written
to non-written, i.e. the top and bottom of the trace. A command which is
sent from the computer to the 7912AD is the "ATC" for average-to-center.
This command causes the 7912AD to find the center value between the two
arrays and fill in any missing points, and then store this new array in
the digitizer's memory. It also displays it on the oscilloscope as a
single trace. If the main intensity is too high, i.e. the trace is too
thick, after the "ATC" command, the displayed peak will be smaller than
it actually is. This means that in setting up the digitizer care must be
taken in adjusting the intensity to make sure the digitized signal is the
same as the monitored height. The pulse pickoff signal is used for this.
Another feature which the 7912AD has is the ability to average
several traces together, thus increasing the signal to noise ratio. The
signal averages 2,4,8,16,32 or 64 traces by adding each waveform to what
is memory. Because each waveform has 9-bit resolution and each value is
sent to the computer as a 2-byte word, no precision is lost in this
averaging mode. This mode is important because both time and memory
storage are saved by compressing the signal-averaged traces into one
waveform. Care must be exercised in choosing the number of pulses per
waveform because of the possibility of washing out the signal from a
minor constituent in the sample.
Scientific Instruments 5500
The 5500 is a microprocessor-based, low temperature, indicator/
controller. It is configured to use a chromel-gold w/.07% Fe
thermocouple. The maximum heater output is 90 watts. All calibration
and control can be done equivalently either from the front panel or over
the computer interface. It has three modes: i) Stop, ii) Manual, and
iii) Run. In the Stop mode, the heater power is shut off and the system
will go to the lowest possible temperature. In the Manual mode the
controller will try to maintain the set point temperature. In the Run
mode, up to a 30-point temperature profile program stored in the 5500's
memory is run. In all three modes, an actual temperature profile can be
graphed on the screen and also output to the Tektronix plotter.
The 5500 was used with the specimen holder used in this study to
determine the cool-down time and ultimate temperature. A heater was not
used. The time required to reach this temperature of 650K is
approximately two hours. The thermocouple in this holder broke after a
short time and was not repaired because of the need to disassemble the
manipulator system. The new holder described in Appendix A has an
improved cryogenic design and a heater is installed.
A program listed in Appendix D was written to input a program into
the 5500, graph the temperature profile data, and change the set point
temperature in the manual mode. The program name is "PROFILER" and it is
stored in the public directory of the 4909 file manager.
The Bertan 205A-30R is a 0-30 kV d.c. power supply. It can be
controlled by the computer when used with the Bertan model 200-C488
interface controller. The controller accepts commands over the bus and
converts them to a 0 to 5 volt output which is fed into the remote
programming input for the 205A-30R. When the local/remote switch in the
rear of the 205A-30R is put in remote, control is done over the
interface. In the local mode, the output is the sum of the panel switch
settings. Since the front panel settings on this supply are discrete and
not continuous, a program was written to control the voltage with the
user-definable keys of the computer. This program is also listed in
Appendix D. The program is "FIMSUPPLY" in the public directory of the
4909. Because the supply is controlled by the computer, the IAP
data-handling program had to be modified to include the voltage controls
with the user-definable keys.
IAP Data Collecting And Handling Programs
The programs described in this section which collect and reduce the
waveforms from the IAP are based on the Tektronix demo programs which
were supplied with the 4052A and 7912AD. The programs evolved from
having the waveform acquisition, storage on magnetic tape, and data
manipulation done with single keystrokes of the user-definable keys to
automatic data acquisition and storage on the 4909 file manager. The
basic program used is "IAPINDEX_4909." This program stores waveforms on
indexed files in the 4909. New indexed files can be created at any time.
Single waveforms can be collected with one keystroke. Waveforms
collected can be chosen to be automatically stored in the next available
index within the file being used. The m/n ratios of peaks are calculated
in two ways: 1) by taking the ratio of the squares of the flight times
of an unknown and a known mass multiplied by the known mass; 2) by
straight TOF calculation using the equation II-1, previously defined.
The values obtained for the selected flight times are compared in table
format. The best results are obtained when the largest mass-to-charge
ratio known is used as the reference.
The "IAPINDEX_4909" program is written in independent sections, each
section being a subroutine which can be addressed either from the
user-definable keys or from within a controlling program. Two programs
which utilize a control program using these subroutines are "IAPRING" and
"PEAKPICKOFF." All control sections start at statement 60000. The
"IAPRING" program collects and stores waveforms continuously. The
"PEAKPICKOFF" program retrieves each waveform which was stored and finds
the Ni signal peak height. "IAPINDEX_4909" is listed in Appendix D. The
two controlling sections are also listed. The modified "IAPRING" program
having the high voltage supply control sections is listed. Its name is
"IAPRING.HV." In this program, all sections of "IAPRING" not required
for data acquisition were removed and sections of "FIMSUPPLY" needed for
controlling the high voltage supply were added. In addition all sections
which are used most frequently are controlled by user-definable keys
1-10; the others required the shift key for 11-20. Table II-1 gives the
User-Defined Key Functions
IAPINDEX 4909 & IAPRING.HV
I 9 .9
Move cursor left
Move cursor right
Read wfm. from file
Graph wfm. @ plotter
Calc. masses (eqn.)
Graph @ screen
Calc. masses (ratio)
Mark TOF times
Change current file
Set left marker
Set right marker
Marker's time dif.
Record wfm. on file
Graph@ plot. w/markers
Ground (DC offset)
Graph@ scrn. w/markers
Increase V by vinc
Reset power supply
Increase V lOOv
Decrease V by vinc
Decrease V lOOv
Move cursor left
Move cursor right
Set V to Ov
Volt. ramp on/off
Incr. vinc by 10%
Incr. inc 10%
Set V to Ov
Decr. inc 10%
Note: Some of these functions can be used when the control sections
(the portions of the IAP-series programs starting at statement number
60000), are running and looping. The result of pressing the key will
not occur until an appropriate point in the program. These points are
normally when the program is going from one subroutine to another.
Non-critical subroutines can be interrupted, but the program returns to
the point where it was interrupted and continues from there.
user-definable keys and their functions for the programs "IAPINDEX_4909",
"IAPRING," "FIMSUPPLY," and "IAPRING.HV."
The ion gun employed in this study is a model G-2-D system from
Colutron Research Corp. This kit comes complete, assembled in a vacuum
housing. It must be configured by the customer with ancillary equipment
such as vacuum pumping system, power supplies and associated insulation
housing, and cooling system for source and electromagnet. This gun was
chosen for this study for several reasons, the most important being
vacuum considerations. The in situ implantation of deuterium to overcome
oxidation and cryogenic transfer problems presents a major difficulty
with Field-Ion techniques, enhanced field adsorption of hydrogen. That
is, during implantation with deuterium, the deuterium partial pressure in
the FIM/IAP chamber must be kept sufficiently low in order that during
subsequent IAP analysis field adsorbed deuterium does not interfere with
the implanted deuterium signal. The ion gun system was designed in order
to keep the FIM/IAP chamber pressure below 5x10 9 Torr during implanta-
tion. Figure II-10 shows the ion gun that is coupled to the FIM/IAP with
associated hardware and electronics. With the experimentally determined
operating parameters of this gun, the pressure in the chamber is
approximately an order of magnitude better than the design limit.
The gun operates with a throughput of approximately 10-' Torr-1/sec.
With the Balzers TSU 170 1/sec turbopump, the pressure during operation
is 5-8x10-6 Torr in the gun and 4-6x102 microns in the source. These
values are typical with the gaseous charges used in the source. Although
the gun is capable of using solid charges, for this study it has only
Figure 11-10 Overall view of the Colutron ion gun and associated
hardware, power supplies, and vacuum equipment. The anode and filament
supplies, thermocouple gauge, and ion source float at high potential and
must be isolated from ground. Cooling of the ion source and the velocity
filter is accomplished with a 1/2 h.p. refrigeration system. Only the
refrigerant lines can be seen in the photograph.
been configured for gases. The pressure loads for solid charges will be
considerably higher and the beam currents will also be less. Additional
differential pumping is done by a 20 1/sec Perkin-Elmer DI ion pump and
titanium sublimation pump connected to the beam line with a flexible
metal hose. Conduction limiting is also done with a 2 mm hole in a
double-sided blank flange mounted before the straight-through valve which
connects to the FIM/IAP chamber. Although the gun is capable of being
baked-out, this is not done due to the difficulty involved with removing
the freon cooling lines to the magnet and ion source.
Another important parameter of this gun which needed to be
considered was current density. A reasonably short time is required for
the implantation, again, because of the above arguments. For gaseous
charges this gun produces ion currents up to about 10 uA. With the
einzel lens in the system, current densities of 1-10 mA/cm2 are easily
achieved. The ion gun also incorporates vertical deflection plates and a
velocity filter. The velocity filter is an ExB type, or Wien filter,
with a horizontal deflection plane. Normal operation for aligning and
selecting an ion of a particular mass-to-charge ratio is done by changing
the voltage on vertical deflection plates and varying the power to the
magnet. The voltage on the horizontal plates are set at maximum supply
output for maximum dispersion. The Colutron filter  differs from a
simple ExB velocity filter in that the electric field is shaped by
electrically biased guard rings about the horizontal deflection plates.
The reason they are needed is that the Wien filter is a strongly
focussing lens and produces a line image with a very short focal length.
This is due to the fringe field shapes of the finite sizes of the magnet
MAGNET 1 1 "
MAGNET U 2 I -
MIDDLE SHIM 3
PLATE 4 -- -- 4 PLATE
SHIM 3 5 3 SHIM 3
SHIM 2 6 BEAM 2 SHIM 2
SHIM i 7 SHIM 1
MAGNET 2 8
Figure II-11 Schematic diagram of Colutron velocity filter. A desired
beam shape is obtained by carefully balancing the voltages on the shims.
The guard ring control unit supplied with the filter is a set of parallel
voltage dividers, each delivering a fraction of the deflection plate
voltage to its respective ring.
and deflection plates. By carefully balancing the potentials on the
various guard rings, the filter can operate in a non-focussing mode in
which a circular beam is produced, or in a line mode with a very narrow
line image. The resolution, M/AM, of this filter is approximately 400.
Figure II-11 is a schematic of the velocity filter.
The use of this velocity filter provides several benefits to this
study. Ions with different mass-to-charge ratios can be separated very
easily. This allows less pure charges or mixtures to be used. In fact
for the gases hydrogen, deuterium, and helium a mixture of 2% argon
stabilizes the plasma and reduces the pressure in the source considerab-
ly. The filter separates the same species with different masses and
charge states. For example, hydrogen can be ionized into H%, H;, and H+
and argon can be ionized in two states, Ar* and Ar*2. The choice of ion
complex, of course, will affect the relative implantation depths. For
example, the depth for H; would correspond to that of H+ at half the
The ion gun was mounted to the FIM/IAP in such a way that it can be
decoupled and used independently. A special holder for FIM specimen is
made from a MDC electrical feedthrough mounted on a Conflat flange. This
holder, shown in Figure 11-12, monitors the current density during
implantation. The grounded shield has a .062" diameter hole in it so
that the current measured multiplied by 50 (the reciprocal of the
cross-sectional area in cm2) is equal to the current density. When the
gun is coupled to the FIM/IAP, the current is measured by disconnecting
the high voltage lead and connecting it to an electrometer. It should be
noted that the current measured at this point is not the actual ion
Figure 11-12 Faraday Cup/Sample Holder. This holder is used on the ion
gun when it is not coupled to the FIM/IAP. If the beam is larger than
the grounded outer shield aperture (piece to right), the beam current
density (A/cm2) is obtained by multiplying the current by 100.
ISOLATED FROM GROUND
ACCELERATION & FOCUSSING PLATES
ANJ i I
Figure 11-13 Schematic diagram of
the Colutron ion gun, beam line, and
current, but also includes secondary electron and ion currents. Both
arrangements, ex situ and in situ, of the FIM/IAP can accommodate both
FIM and TEM samples. SEM samples can also be used but there is a
restriction on their physical size because of specimen transfer
The beam line has a transmission phosphor screen with a hole and a
mirror for viewing, selecting and aligning the beam to be used. There is
a Faraday cup which swings into the beam and can monitor the current and
current density. The hole diameter of the tantalum grounding front
shield is .140" such that if the beam is centered and larger than this,
the current at the cup is multiplied by a factor of 10 to give the
current density. This cup is used to optimize the beam conditions. The
ion source pressure and anode voltage is adjusted for maximum beam
Figure 11-13 shows a schematic diagram of the ion gun, beam line,
and target. The filament and anode power supplies are Lambda model
LK-351 and two LQ-524 (connected in series). These supplies together
with the thermocouple gauge controller for the source are isolated from
ground by a Colutron isolation transformer. This transformer is rated
for 10 kV at 1 kVA. Field testing of this transformer has shown it to be
capable of operation up to 22 kV. This value is the break-down voltage
between the ion source flange and the ion gun body. Two Brandenburg 30kV
power supplies provide the acceleration and einzel focussing voltage. A
Colutron power supply contains three separate variable, regulated voltage
supplies: a -100 to +100 V supply for the vertical deflection plates, a
0 to 300 V supply for horizontal plates, and a 30V-30A magnet supply.
For low Z ions with energies greater than 9 keV, an additional 45 V is
required for the vertical plate voltage. A box containing five 9-volt
transistor batteries in series is inserted in series with the above
supply. The currents at the target and cup are measured by Keithley
model 600B electrometers.
Mass Identification in the Colutron Ion Gun
A major advantage of the Colutron ion gun with the velocity filter
is that gas mixtures may be present in the gun whether deliberately mixed
for better performance or as the result of changing gases without
prolonged purging of the lines. In selecting a beam with a particular
mass to charge ratio by using the velocity filter, there sometimes is
confusion as to the identity of the various beams. The low end masses
are readily sorted out at a given energy by comparing the beams of the
helium/argon and deuterium/argon mixtures. The He* and D; signals have
the same mass to charge ratio and therefore the same magnet setting.
Both gas mixtures have the Ar+ and Ar+2 signals when hydrogen and
deuterium are present in the ion source, four beams are present having
m/n = 1,2,3 and 4 (H+, H2 or D', H+ or HD, and D0). In addition, the
Ar peak is always present when the gas mixtures are used, and the Ar
peak is usually the largest mass present, having the highest magnet
The masses are tuned with the velocity filter by changing the
magnetic field. The following expression holds true for determining the
masses in the velocity filter,
B,/B, = (m2/m1)1/2 II-2
where Bi is the magnetic field to balance the filter for mass, mi. The
magnetic field is proportional to the magnet current which in turn is
proportional to the dial setting on the Colutron magnet power supply.
Because of hysteresis effects, there is a constant offset current which
needs to be added to the measured current. This setting which is the sum
of the value read and the offset value is referred to as the true
setting, S. Thus the following can be used in place of equation 11-2,
S2/S, = (m2/m1)1/2 11-3
It should be noted that the difference between two true settings and the
measured settings is the same. Therefore rearranging equation 11-3,
S2/SI SI/Sl = (m2/m1)1/2 1 11-4
AS/SI = (m2/ml)1/2 1 11-5
By knowing two or more masses in the beam, a reference true setting for
one of the masses can be found,
S, = AS/(m2/ml)1/2-1 11-6
The true setting for mass, mi, can be found with two masses, or an
averaged S, could also be found using other known masses. If mi is
chosen as HI (mi = 1), then equation 11-6 reduces to
SH = Rm2-RH/(m2)1/2-1, 11-7
where Rm2 and RH are the measured settings of m2 and H, respectively.
Once SH is found, unknown masses are easily identified by
rearranging equation 11-7 and solving for mx, leading to
mx = [Rmx-RH/SH + 1]2, 11-8
where mx refers to the unknown mass at the measured setting Rmx.
The program, "COLUMASS", is available on the Tektronix 4052A which
will find both SH for a given energy and an unknown mass for a particular
setting. If more than two masses are known an averaged SH value is
found. Table 11-2 gives the values of SH at several energies and the
differences between the mass setting values for the indicated ions and
the setting for H*.
Transmission Electron Microscopy
Three different holders have been designed and used for TEM imaging
of field emitters in this study. The use of the TEM is indispensable for
obtaining the geometric parameters required for the depth profiling
programs which will be described in the next chapter. It also provides
an independent means of checking the total depth which has been field
evaporated during a profiling experiment. In addition, the TEM is
unsurpassed in obtaining crystallographic information about defects on a
fine scale with the use of diffraction contrast. In the following
sections, each of the three different holders will be presented and their
uses with respect to FIM studies will be discussed.
Hydrogen and Relative Magnet Settings for
Several Ions and Energies
Difference Between Ion And H* Setting
5 50.1 24.1 22 36 48 198
6 45.6 22.5 19 35 43 -- 184
7 44.1 25.1 18 35 41 -- 176
8 39.4 24.9 14.5 30.5 41.5 -- 159
9 30.0 26.0 13 22 30 126 156
10 31.3 18.3 12.6 22 32.5 -- 133
FIM/IAP "Bulk" Holder
Figure 11-14 shows a simple holder for use with the JEOL-SCSH bulk
holder. This holder provides a single tilt axis about the specimen's
Figure 11-14 FIM/TEM "BULK" specimen holder. This holder has only a
single axis of rotation. Shown also is the sample insert which actually
holds the specimen.
FIM/TEM "Double-tilt" specimen holder. This holder has
tilt axes and is required when specific crystallographic
axis. This holder is useful when routine observation is desired, such as
checking specimen quality after preparation or after implantation. When
several of these holders are available, specimen throughput in terms of
the cycle time required to obtain a two-beam imaging condition, record a
micrograph, and insert a new sample is on the order of 15 to 20 minutes.
A two-beam imaging condition is important when imaging FIM specimens
because the penetration of the electrons is deeper due to dynamical
conditions. The value of this holder is limited when crystallographic
information is required. This is due to having only a single-tilt axis
available. Because most FIM specimens are prepared from drawn wire, they
have a preferred orientation along this axis. The orientation is a
usually a low-index pole parallel to this axis. For example, nickel
(FCC) has a (111) orientation, platinum (FCC) has a (001), and tungsten
(BCC) has a (011). The attainment of a two-beam condition is relatively
easy to achieve because of this, but the choice of the imaging condition
is determined purely by chance. Studies such as the determination of
defects are impossible with this type of holder because of the lack of a
second, orthogonal, tilt axis.
FIM/TEM "Double-Tilt" Holder
The above problems with defect identification using diffraction
contrast have been remedied by the construction of another TEM/FIM holder
which incorporates the second tilt axis . Figure 11-15 shows this
specimen holder. It is a modified standard JEOL-BST double-tilt holder.
Both the original cups were removed and some machining of the rod was
done to accommodate a single-elongated holder for FIM samples. The
double-tilt is achieved by two rods applying friction to the cup as they
Figure II-16 Partial kikuchi map of a Ni specimen showing the extent of
tilt available with the "Double-tilt" holder of Figure 11-15.
move in and out thus tilting the cup. Figure 11-16 is a portion of a Ni
Kikuchi map illustrating the tilt capabilities of this holder.
Approximately 270 on the second axis is available with this holder.
Two-beam conditions of various different orientations, can be obtained
and defect characterization can be done by using the *-b=0 criteria.
This type of analysis was done on a dislocation found in a Ni specimen
. Figure 11-17 shows two two-beam conditions, 2=(111) and (111) of
this sample. In Figure II-17b, *-b=O and the dislocation is not visible.
The (111) case was imaged close to the  zone axis while the (111)
case was imaged close to the  zone axis. This illustrates the
usefulness of this holder in obtaining the desired crystallographic
FIM/TEM "Field-Effect" Holder
The third TEM/FIM holder is shown in Figure 11-18. This
field-effect holder has only a single axis of tilt, but is capable of
having up to approximately 5 kV applied to the sample in situ in the TEM.
This holder was designed and constructed by Panitz*, but was first used
by this author  to study the effect of field-induced stresses in
emitters. This holder was found to have some peculiar operating
characteristics. If the holder is used without a cable connecting the
high voltage supply, the image would oscillate slowly. This was probably
a charging effect because when a grounding connector was used on the end
of it, the oscillations ceased. If the cable is attached and the power
turned off, the image is again unstable and drifts. Turning the supply
on and applying approximately 10 v stabilizes the image. Care must be
*Panitz, J. A., private communication.
a .. i
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4-- In oi.-
w r- C U
0 U w-
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X- -0 -II r
Figure 11-18 FIM/TEM "Field-Effect" holder. Voltages between 0-5 kV
can be applied to FIM specimens in situ TEM with this holder. Only a
single rotation axis is available.
taken that the weight of the excess cable does not affect the mechanical
stability of the stage. When applying relatively low voltages (up to 1.0
kV) to the emitter, the tip can still be imaged, but both mechanical and
beam positioning must be done and extreme beam settings (e.g.,condenser
and stigmater lens) must be done. Above approximately 1.1 kV an apparent
"hole" forms at the apex of the specimen due to the electric field. As
the field is increased, the "hole" gets larger and the specimens appear
to disappear into it. Figure 11-19 is a sequence of increasing voltage
depicting this. Because of this, the results of applying the field to
the sample in the TEM can not be seen while the voltage is on. Because
field evaporation is a thermally activated process, the application of
3 kV to a specimen in this holder will result in a field evaporation
voltage of about 13 kV if it would be returned to the FIM. For this
reason, voltages above 3 kV should be avoided in the TEM. Figure 11-20
is an example of the results of applying 3 kV to the Ni specimen
containing the dislocation in Figure 11-17. It is seen that the
field-induced stresses have caused the dislocation to sweep through the
sample. A faint slip trace can be seen in Figure II-20b and approxi-
mately 20 nm has been field evaporated.
The field effect holder will surely prove to be a valuable aid in
future metallurgical applications of FIM techniques. Studies using this
holder will be able to answer the most often asked question, what is the
effect of the applied field to the sample?
Another major use for this holder will be to expose features of
interest such as grain boundaries or precipitates to the surface for
imaging in the FIM. This holder, in conjunction with back-polishing
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techniques developed by Nord6n et al. [78,79], will help overcome one of
the major disadvantages of FIM techniques, specimen size. Because of the
extremely small volume accessible to analysis, features of interest are
extremely difficult to find and, in general, many samples are required to
be examined. This is true even when these features are present in large
quantities, e.g., samples with high dislocation densities or extremely
fine grain size for grain boundaries. In general, the geometry of FIM
specimens is ideal for observation in the TEM. In addition, this
field-effect holder can create experimentally controllable stress states
which are similar to the conditions found in the volume just ahead of a
crack tip in an embrittled alloy.
Depth Profiling Using The FIM/IAP
This chapter deals with experiments designed to establish the
validity of the procedures developed in this study. Without such
experiments, a complete FIM/IAP study of the ion implantation into
materials, especially the trapping of deuterium to implanted defects,
would not be feasible or believable. In addition to these control
experiments, the procedures for reducing the raw IAP data from implanted
specimens will be presented. The actual results of implanted specimens
will be given in Chapter IV.
This chapter will be divided into three main sections: 1) "Depth
Profilng Using The FIM/IAP", 2) "Effects Of Field Ionization And
Evaporation", and 3) "Special Problems Associated With
Hydrogen/Deuterium." Each section is important with respect to the
proper operation of the FIM/IAP and interpretation interpretation of
experimental results. The section on depth profiling in the FIM/IAP
will demonstrate a method for establishing a depth scale for extended
profiles when an imaging gas is not present. Such studies have not been
possible to date and are critical for emitters with relatively low field
evaporation fields. The section on the effects of high fields gives some
of the answers to questions which are always raised about their effect on
defect microstructures. There is reason for considerable optimism that
some defects induced by implantation are unaffected by field induced
stresses. The section on the special problems of hydrogen/deuterium will
show that in situ implantation is indeed feasible. Field adsorbed D can
be reliably distinguished from implanted D. This section will also
present some observations of a more general interest to FIM studies but
which also of importance to this study. Some of these are important to
proper operation of the FIM/IAP and/or analyzing the data correctly. It
should be born in mind that there are still fewer than twenty of these
instruments worldwide, nearly all individually designed and built.
Therfore, it is important that this type of information be disseminated.
Ring Counting Experiments
It is extremely important to be able to accurately depth profile
implanted species. Depth profiling is the forte of FIM in conjunction
with the atom probe. During evaporation, with an imaging gas present,
each ring of atoms constituting an atomic plane, appears to collapse and
disappear as evaporation proceeds. Each ring collapse of a particular
set of planes denotes a precise distance probed equivalent to that
d-spacing. This is the most accurate profiling method which exists,
providing, of course, that one can observe these ring collapses implying
that an imaging gas is present. In investigations which require UHV
conditions during analysis (i.e. without an imaging gas), such as the
present one, the rings can neither be seen nor directly counted. It was
thus necessary to develop another method of ascertaining the depth.
Further complications arise with respect to the IAP spectra, since
the signals vary in strength even when the voltages are held constant.
For shallow depth profiles a sudden increase in peak height indicates a
ring collapse. Counting these gives the same accuracy as with counting
the rings visually. This method is impractical for larger depths, such
as those needed for ion implantation studies, typically 100 nm or more.
This is because the voltages need to be raised many times in such a
profiling experiment, and it is extremely difficult to differentiate
reliably an increased pulse height due to a ring collapse or from an
increased evaporation rate. Furthermore, up to 30 thousand pulses may be
required to evaporate to the required depth on the order of 100 nm or so.
It would be very tedious to sort through such a mountain of data in order
to determine all the occurrences of ring collapses.
In Chapter II major requirements were cited for establishing a
suitable procedure for extended depth profiles with the IAP. The first
is that the method must be able to reduce the number of spectra to
manageable levels. Consider a typical example: the amount of storage
required if 30 thousand spectra are to be stored. (Because of the
requirement for rapid pulsing the spectra must be collected and stored;
analyzing them in real time requires too much time.) Each spectrum takes
about 5 kbytes of disk storage. Thus for the 30 thousand spectra, over
100 Mbytes of storage is required! The signal-averaging mode of the
Tektronix 7912AD alleviates this problem somewhat. The 7912AD can
average 2,4,8,16,32 or 64 traces, thus reducing the storage requirement
by the factor chosen. The second point, is that the method chosen for
depth profiling must be insensitive to the field evaporation rate.
During an extended profiling experiment the field evaporation rate will
of course change widely, both while the voltage is being held constant
(giving a decaying rate of field evaporation) and when the voltage is
increased (leading to an increased rate of field evaporation).
In the remainder of this chapter the method chosen for the depth
profiling requirements of this study are described in detail. It relies
upon the geometry of field emitters observed by TEM, the basic principles
of operation of the FIM, and a particular calibration procedure.
The tip geometry assumed to apply for this study is a conical shank
with a spherical cap at the apex. The spherical cap joins the shank
tangentially, i.e. a radius vector from the center of curvature to this
point is perpendicular to the shank. In the FIM only a portion of the
specimen is imaged. Figure III-1 shows the assumed geometry of a
specimen. The cross-hatched region represents the probed volume of our
instrument with a subtended viewing half-angle of 200. With
this model, the radius of curvature is given as
where 1l is the distance from the initial surface, a is the shank
half-angle and h is the distance probed from the initial surface to the
final surface. Figure III-2 is a montage of an evaporation sequence of a
Ni specimen performed with the "field-effect" (FIM/TEM) holder. This
figure illustrates two points, the geometric model is quite valid and the
distance which the FIM/IAP is capable of probing is considerable (>1 um).
The computer-generated figure was done using equation III-1. The
parameter, a, was measured from the montage. Using the Tektronix 4662
-LO I ---h
Figure III-1 Assumed geometry of emitter. Cross-hatched region
indicates volume probed by IAP. The distance h is the depth probed from
the initial surface to the second surface.
FIELD EVAPORATION OF A Ni EMITTER TO 3kV in-situ TEM
0 0.9 1 .3 1 7 2.1 2.5 3 0
0 7 1 1 5 1 9 2.3 2.7
APPLIED VOLTAGES (kV)
Figure III-2 Montage of TEM micrographs field evaporated in situ TEM in
the FIM/TEM "Field-Effect" holder. Also shown for comparison is a
computer-generated sequence using the model for the tip geometry
discussed in text.
plotter, each radius was drawn at the measured distance from the apex of
the cone (equal to 10 in equation III-1). The computed radii at the
various voltages in Figure III-2 are all very close to the actual radii
from the micrographs except one, the radius drawn at the indicated
voltage of 3 kV. This radius was measured from the micrograph and drawn
at the distance given by equation III-1. When it was drawn by the
computer, it did not match the location in the montage. After examining
the montage more carefully, it was found that one micrograph, taken at
2.9 kV was missing. The last micrograph in the sequence had been
positioned a little too far to the left. The offset between the surface
drawn and the one in the montage is approximately the displacement due to
this error. It should be pointed out that this error was not found until
after the application of equation III-1 in generating the figure. This
suggests a precision of better than 10 nm.
IAP probed-volume considerations
For the Chevron plates used as the detector in the IAP, it has
already been shown that the detector efficiency and gain is constant over
the energy range and for the types of ions employed here .
Furthermore, it is the detector which limits the width of the area probed
indicated in Figure III-1. If all the atoms within that volume strike
the detector and the detector efficiency is constant, the integrated
signal should be proportional to the number of atoms contained within the
probed volume. The number of atoms within this volume is simply related
to the volume by the density of the specimen. This model is the
foundation for the method used to determine depths in this study. That
is, it is assumed that the integrated bulk signal from the Chevron
detector is proportional to the volume probed. The integrated signal is
easy to measure, since it is just the cumulative matrix signal from the
spectra collected. The accumulation of spectra approximates an
integration very closely because of the small step involved with a ring
collapse, and that it can take many pulses to evaporate one layer. The
one assumption made with this method is that the concentration of the
element used for the accumulation process is constant and is proportional
to the probed volume. There may be situations for which this assumption
is not valid, e.g. ion implantation of massive ions or the presence of
precipitates, but for ion implanted deuterium into nickel, this
assumption is certainly reasonable.
The problem of depth profiling using the model just described is
reduced to finding the functional dependence of the volume with depth
and geometrical parameters of the specimen. Then to compare these with a
calibration experiment in which the rings are counted and the cumulative
signal is found from the spectra.
The calculation of the probed volume is straight-forward.
Figure III-3 shows a representation of the cross-hatched volume in
Figure III-1. The volume of interest is the shaded region bounded by the
two spherical caps representing the initial and final surfaces, and the
sides of the cone representing the limit of the area of the emitter
surface projected onto the detector. The bases for the spherical caps
are indicated by dotted lines. This volume can be seen to be
V = V, + V2 V3
Figure 111-3 Representation of the volume probed by the FIM/IAP in an
emitter. The shaded area corresponds to the cross-hatched area in
where V, is the volume of the frustrum of the cone bounded top and bottom
by the dotted lines, V2 is the spherical cap of radius Ro, and V3 is the
spherical cap of radius R. The value h is equal to the number of planes
evaporated normal to the emitter's axis, (N dhkl). Using equation
III-1, the radii of curvature can be expressed as
Ro= lo*sina/(l-sina) III-3a
R= (h+10o)sina/(1-sina) III-3b
The equation for the volume of a spherical cap subtended by an angle,
3, and radius, Rc is
Vs.c.= *Rc(2-3cosB +cos30) III-4
Using this formula, V2 and V3 are given as
V2= *Ka 3l (2-3cosp +cos3 ) III-5a
V3= 3 *K3.[h3+3h210 +3hl2 +13]*(2-3cosp +cos3P) III-5b
where Ka= sina/(1-sina), and 1o is defined above. Using equations III-5a
V2-V3= 3 -K3-[h3 +3h210 +3hl2]*(2-3coso +cos30) III-6
The volume of a frustrum of a cone is given as
VF= *Z-(RT +RB +RTRB) 111-7
where RT and RB are the radii of the top and bottom areas, and Z is the
height of it. For V1, RT= RosinB, and for V3, RB= RsinB. Using
equations III-3 and substituting into equation III-7 and doing a little
algebra, V, is given as
V= -[K2sin2 +K3(1-cos3)sin23]*[h3 +3h210 +3hl2] III-8
Substituting III-8 and III-6 into III-2, and simplifying the coefficient
V= .[K2sin2 -K3.(1-cosp)2].[h3 +3h210 +3hl] III2-9
This is the probed volume to which the cumulated matrix signal is
proportional. The parameters needed for each specimen to be found are the
shank half-angle, a, and lo, the initial surface to apex of the cone made
by extending the sides of the emitter to their point of convergence. The
system parameters to be determined are the detector viewing half-angle,
3, and the proportionality constant between the volume and the
accumulated signal. This constant, KD, has several other constants
within: the emitter density, the efficiency of the detector, the gain of
the detector, the gain of the amplifier, etc. Determination of KD will
be discussed in a later section.
Determination of P
For the depth evaporated in an IAP experiment the viewing
half-angle, 0, is assumed constant. The reason for this can be explained
by considering the FIM image. The image is a projection of the surface
of the tip onto the screen. This projection is similar to a stereo-
graphic projection in that the projection point is close to that used in
a stereographic projection . With this pseudo-stereographic
projection, the angular positions between poles of crystal planes are
still approximately constant at all radii. This is true even though the
radius of curvature is increasing as the emitter is field evaporated
since the radius of the emitter is much smaller than the radius of the
sphere of projection. It can be understood by considering the distance
the projection point changes with depth (on the order of 1 um) as
compared to the projection distance (on the order of 10 cm). The only
difference between low and high voltage images of the same tip is the
appearance of higher-indexed planes as the radius increases. The
invariance of the motion of the relative positions of the major poles
present at all radii can be observed by d.c. field evaporation. The
value of 3 can be determined in the same manner as FIM micrographs are
indexed . Figure III-4 shows an indexed micrograph of a Ni emitter.
The viewing screen angle can be found from the following relationship,
20 = (Dscreen/D(111),(113))'8(111),(113) III-10
where Dscreen is the measured diameter of the total viewing area of the
micrograph, D(111),(113) is the measured distance and 8(111),(113) the