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Scanning Electron
Microscopy and
X-Ray Microanalysis
Joseph I. Goldstein
Dale E. Newbury
Joseph R. Michael
Nicholas W.M. Ritchie
John Henry J. Scott
David C. Joy
Fourth Edition

Scanning Electron Microscopy and X-Ray Microanalysis

Joseph I. Goldstein
Dale E. Newbury
Joseph R. Michael
Nicholas W.M. Ritchie
John Henry J. Scott
David C. Joy
Scanning Electron
Microscopy and
X-Ray Microanalysis
Fourth Edition

ISBN 978-1-4939-6674-5 ISBN 978-1-4939-6676-9 (eBook)
https://doi.org/10.1007/978-1-4939-6676-9
Library of Congress Control Number: 2017943045
© Springer Science+Business Media LLC 2018
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The registered company address is: 233 Spring Street, New York, NY 10013, U.S.A.
Joseph I. Goldstein
University of Massachusetts
Amherst, MA, USA
Joseph R. Michael
Sandia National Laboratories
Albuquerque, NM, USA
John Henry J. Scott
National Institute of Standards and Technology
Gaithersburg, MD, USA
Dale E. Newbury
National Institute of Standards and Technology
Gaithersburg, MD, USA
Nicholas W.M. Ritchie
National Institute of Standards and Technology
Gaithersburg, MD, USA
David C. Joy
University of Tennessee
Knoxville, TN, USA

V
Preface
This is not your father’s, your mother’s, or your
grandparent’s Scanning Electron Microscopy and
X-Ray Microanalysis (SEMXM). But that is not to
say that there is no continuity or to deny a family
resemblance. SEMXM4 is the fourth in the series
of textbooks with this title, and continues a tradi-
tion that extends back to the “zero-th edition” in
1975 published under the title, “Practical Scanning
Electron Microscopy” (Plenum Press, New York).
However, the latest edition differs sharply from
its predecessors, which attempted an encyclope-
dic approach to the subject by providing extensive
details on how the SEM and its associated devices
actually work, for example, electron sources, lenses,
electron detectors, X-ray spectrometers, and so on.
In constructing this new edition, the authors have
chosen a different approach. Modern SEMs and the
associated X-ray spectrometry and crystallography
measurement functions operate under such exten-
sive computer control and automation that it is
actually difficult for the microscopist-microanalyst
to interact with the instrument except within care-
fully prescribed boundaries. Much of the flexibility
of parameter selection that early instruments pro-
vided has now been lost, as instrumental operation
functions have been folded into software control.
Thus, electron sources are merely turned “on,” with
the computer control optimizing the operation, or
for the thermally assisted field emission gun, the
electron source may be permanently “on.” The user
can certainly adjust the lenses to focus the image,
but this focusing action often involves complex
interactions of two or more lenses, which formerly
would have required individual adjustment. More-
over, the nature of the SEM field has fundamentally
changed. What was once a very specialized instru-
ment system that required a high level of training
and knowledge on the part of the user has become
much more of a routine tool. The SEM is now sim-
ply one of a considerable suite of instruments that
can be employed to solve problems in the physical
and biological sciences, in engineering, in technol-
ogy, in manufacturing and quality control, in fail-
ure analysis, in forensic science, and other fields.
The authors also recognize the profound changes
that have occurred in the manner in which peo-
ple obtain information. The units of SEMXM4,
whether referred to as chapters or modules, are
meant to be relatively self-contained. Our hope
is that a reader seeking specific information can
select a topic from the list and obtain a good
understanding of the topic from that module
alone. While each topic is supported by informa-
tion in other modules, we acknowledge the like-
lihood that not all users of SEMXM4 will “read
it all.” This approach inevitably leads to a degree
of overlap and repetition since similar informa-
tion may appear in two or more places, and this is
entirely intentional.
In recognition of these fundamental changes, the
authors have chosen to modify SEMXM4 exten-
sively to provide a guide on the actual use of the
instrument without overwhelming the reader with
the burden of details on the physics of the opera-
tion of the instrument and its various attachments.
Our guiding principle is that the microscopist-
microanalyst must understand which parameters
can be adjusted and what is an effective strategy to
select those parameters to solve a particular prob-
lem. The modern SEM is an extraordinarily flex-
ible tool, capable of operating over a wide range
of electron optical parameters and producing
images from electron detectors with different sig-
nal characteristics. Those users who restrict them-
selves to a single set of operating parameters may
be able to solve certain problems, but they may
never know what they are missing by not explor-
ing the range of parameter space available to them.
SEMXM4 seeks to provide sufficient understand-
ing of the technique for a user to become a com-
petent and efficient problem solver. That is not to
say that there are only a few things to learn. To
help the reader to approach the considerable body
of knowledge needed to operate at a high degree
of competency, a new feature of SEMXM-4 is the
summary checklist provided for each of the major
areas of operation: SEM imaging, elemental X-ray
microanalysis, and backscatter-diffraction crystal-
lography.
Readers familiar with earlier editions of SEMXM
will notice the absence of the extensive material
previously provided on specimen preparation.
Proper specimen preparation is a critical step in
solving most problems, but with the vast range of
applications to materials of diverse character, the
topic of specimen preparation itself has become
the subject of entire books, often devoted to just
one specialized area.

VI
Throughout their history, the authors of the
SEMXM textbooks have been closely associated
as lecturers with the Lehigh University Summer
Microscopy School. The opportunity to teach and
interact with each year’s students has provided a
very useful experience in understanding the com-
munity of users of the technique and its evolution
over time. We hope that these interactions have
improved our written presentation of the subject
as a benefit to newcomers as well as established
practitioners.
Finally, the author team sadly notes the passing in
2015 of Professor Joseph I. Goldstein (University
of Massachusetts, Amherst) who was the “found-
ing father” of the Lehigh University Summer
Microscopy School in 1970, and who organized
and contributed so extensively to the microscopy
courses and to the SEMXM textbooks throughout
the ensuing 45 years. Joe provided the stimulus to
the production of SEMXM4 with his indefatigable
spirit, and his technical contributions are embed-
ded in the X-ray microanalysis sections.
Dale E. Newbury
Nicholas W.M. Ritchie
John Henry J. Scott
Gaithersburg, MD, USA
Joseph R. Michael
Albuquerque, NM, USA
David C. Joy
Knoxville, TN, USA
The original version of this book was revised. Index has been updated.
Preface

VII
Scanning Electron Microscopy and Associated
Techniques: Overview
Imaging Microscopic Features
The scanning electron microscope (SEM) is an
instrument that creates magnified images which
reveal microscopic-scale information on the size,
shape, composition, crystallography, and other
physical and chemical properties of a specimen.
The principle of the SEM was originally demon-
strated by Knoll (1935; Knoll and Theile 1939)
with the first true SEM being developed by von
Ardenne (1938). The modern commercial SEM
emerged from extensive development in the 1950s
and 1960s by Prof. Sir Charles Oatley and his
many students at the University of Cambridge
(Oatley 1972). The basic operating principle of
the SEM involves the creation of a finely focused
beam of energetic electrons by means of emission
from an electron source. The energy of the elec-
trons in this beam, E
0
, is typically selected in the
range from E
0
= 0.1 to 30 keV). After emission
from the source and acceleration to high energy,
the electron beam is modified by apertures, mag-
netic and/or electrostatic lenses, and electromag-
netic coils which act to successively reduce the
beam diameter and to scan the focused beam in a
raster (x-y) pattern to place it sequentially at a
series of closely spaced but discrete locations on
the specimen. At each one of these discrete loca-
tions in the scan pattern, the interaction of the
electron beam with the specimen produces two
outgoing electron products: (1) backscattered
electrons (BSEs), which are beam electrons that
emerge from the specimen with a large fraction of
their incident energy intact after experiencing
scattering and deflection by the electric fields of
the atoms in the sample; and (2) secondary elec-
trons (SEs), which are electrons that escape the
specimen surface after beam electrons have
ejected them from atoms in the sample. Even
though the beam electrons are typically at high
energy, these secondary electrons experience low
kinetic energy transfer and subsequently escape
the specimen surface with very low kinetic ener-
gies, in the range 0–50 eV, with the majority below
5 eV in energy. At each beam location, these out-
going electron signals are measured using one or
more electron detectors, usually an Everhart–
Thornley “secondary electron” detector (which is
actually sensitive to both SEs and BSEs) and a
“dedicated backscattered electron detector” that is
insensitive to SEs. For each of these detectors, the
signal measured at each individual raster scan
location on the sample is digitized and recorded
into computer memory, and is subsequently used
to determine the gray level at the corresponding
X-Y location of a computer display screen, form-
ing a single picture element (or pixel). In a con-
ventional-vacuum SEM, the electron-optical
column and the specimen chamber must operate
under high vacuum conditions (<10
−4
Pa) to min-
imize the unwanted scattering that beam elec-
trons as well as the BSEs and SEs would suffer by
encountering atoms and molecules of atmo-
spheric gasses. Insulating specimens that would
develop surface electrical charge because of
impact of the beam electrons must be given a con-
ductive coating that is properly grounded to pro-
vide an electrical discharge path. In the variable
pressure SEM (VPSEM), specimen chamber pres-
sures can range from 1 Pa to 2000 Pa (derived
from atmospheric gas or a supplied gas such as
water vapor), which provides automatic discharg-
ing of uncoated insulating specimens through the
ionized gas atoms and free electrons generated by
beam, BSE, and SE interactions. At the high end
of this VPSEM pressure range with modest speci-
men cooling (2–5 °C), water can be maintained in
a gas–liquid equilibrium, enabling direct exami-
nation of wet specimens.
SEM electron-optical parameters can be optimized
for different operational modes:
1. A small beam diameter can be selected for high
spatial resolution imaging, with extremely fine
scale detail revealed by possible imaging strate-
gies employing high beam energy, for example,
. Fig. 1a (E
0
= 15 keV) and low beam energy,
. Fig. 1b (E
0
= 0.8 keV), . Fig. 1c (E
0
= 0.5 keV),
and . Fig. 1d (E
0
= 0.3 keV). However, a nega-
tive consequence of choosing a small beam
size is that the beam current is reduced as the
inverse square of the beam diameter. Low beam
current means that visibility is compromised
for features that produce weak contrast.
2. A high beam current improves visibility of low
contrast objects (e.g., . Fig. 2). For any combi-
nation of beam current, pixel dwell time, and
detector efficiency there is always a threshold
contrast below which features of the speci-
men will not be visible. This threshold contrast
depends on the relative size and shape of the
feature of interest. The visibility of large objects
and extended linear objects persists when
small objects have dropped below the visibility

VIII
threshold. This threshold can only be lowered
by increasing beam current, pixel dwell time,
and/or detector efficiency. Selecting higher
beam current means a larger beam size, caus-
ing resolution to deteriorate. Thus, there is a
dynamic contest between resolution and visibil-
ity leading to inevitable limitations on feature
size and feature visibility that can be achieved.
3. The beam divergence angle can be minimized
to increase the depth-of-field (e.g., . Fig. 3).
With optimized selection of aperture size and
specimen-to-objective lens distance (work-
ing distance), it is generally possible to achieve
small beam convergence angles and therefore
effective focus along the beam axis that is at
least equal to the horizontal width of the image.
a
c
b
d
100 nm
YK
EHT - 15.00 kV
WD - 1.7 mm
Signal A = InlLens
I Probe - 135 pAESB Grid = 800 VImage Pixel Size - 1.184 nm
HV mag HFW WD 500 nm
Helios100 000 x
200nm
100nm
x500,0000.30kV UED
10nmJEOL
GBSHWD 2.0mm
SU8200 0.50kV-D 1.6mm X 200k SE+BSE(TU)
SU8200 0.50kV-D 1.6mm X 500k SE+BSE(TU)
1.49 µm990.7 µm800.00 V
Mag - 94.28 K XW idth - 1.213 mm Date: 19 Oct 2015
Signal B = InlLens
. .Fig. 1 a High resolution SEM image taken at high
beam energy (E
0
= 15 keV) of a finFET transistor (16-nm
technology) using an in-lens secondary electron detector.
This cross section was prepared by inverted Ga FIB milling
from backside (Zeiss Auriga Cross beam; image courtesy
of John Notte, Carl Zeiss); Bar = 100 nm. b High resolu-
tion SEM image taken at low beam energy (E
0
= 0.8 keV) of
zeolite (uncoated) using a through-the-lens SE detector
(image courtesy of Trevan Landin, FEI); Bar = 500 nm. c
Mesoporous silica nanosphere showing 5-nm-diameter
pores imaged with a landing energy of 0.5 keV (specimen
courtesy of T. Yokoi, Tokyo Institute of Technology; images
courtesy of A. Muto, Hitachi High Technologies); Upper image
Bar = 200 nm, Lower image Bar = 100 nm. d Si nanoparticle
imaged with a landing energy of 0.3 keV; Bar = 10 nm
(image courtesy V. Robertson, JEOL)
Scanning Electron Microscopy and Associated Techniques: Overview

IX
A negative consequence of using a small aper-
ture to reduce the convergence/divergence angle
is a reduction in beam current.
Vendor software supports collection, dynamic
processing, and interpretation of SEM images,
including extensive spatial measurements. Open
source software such as ImageJ-Fiji, which is
highlighted in this textbook, further extends these
digital image processing capabilities and provides
the user access to a large microscopy community
effort that supports advanced image processing.
General specimen property information that
can be obtained from SEM images:
1. Compositional microstructure (e.g., . Fig. 4).
Compositional variations of 1 unit differ-
ence in average atomic number (Z) can be
observed generally with BSE detection, with
even greater sensitivity (ΔZ = 0.1) for low
(Z = 6) and intermediate (Z = 30) atomic num-
bers. The lateral spatial resolution is generally
limited to approximately 10–100 nm depend-
ing on the specimen composition and the
beam energy selected.
2. Topography (shape) (e.g., . Fig. 5). Topo-
graphic structure can be imaged with varia-
tions in local surface inclination as small as
a few degrees. The edges of structures can
be localized with a spatial resolution rang-
ing from the incident beam diameter (which
can be 1 nm or less, depending on the elec-
tron source) up to 10 nm or greater, depend-
ing on the material and the geometric nature
of the edge (vertical, rounded, tapered, re-
entrant, etc.).
3. Visualizing the third dimension (e.g., . Fig. 6).
Optimizing for a large depth-of-field permits
visualizing the three-dimensional structure
of a specimen. However, in conventional X-Y
image presentation, the resulting image is a
projection of the three dimensional informa-
tion onto a two dimensional plane, suffering
0.5 nA 20 nA
BSE MAG: 1000 x HV: 20.0 kV WD: 11.0 mm BSE MAG: 1000 x HV: 20.0 kV WD: 11.0 mm
20 mm 20 mm
. .Fig. 2 Effect of increasing beam current (at constant pixel dwell time) to improve visibility of low contrast features.
Al-Si eutectic alloy; E
0
= 20 keV; semiconductor BSE detector (sum mode): (left) 0.5 nA; (right) 20 nA; Bar = 20 µm
BSE MAG: 750 x HV: 20.0 kV WD: 11.0mm
4
3
1
2
10 mm
. .Fig. 4 Atomic number contrast with backscattered
electrons. Raney nickel alloy, polished cross section;
E
0
= 20 keV; semiconductor BSE (sum mode) detector. Note
that four different phases corresponding to different com-
positions can be discerned; Bar = 10 µm
HV WD magdetmodeHFW
NIST FEG ESEM11.7 mm
4 mm
CustomETD12 711 x20.00 kV8.0 mm
. .Fig. 3 Large the depth-of-focus; Sn spheres;
E
0
= 20 keV; Everhart–Thornley(positive bias) detector;
Bar = 4 µm (Scott Wight, NIST)
Scanning Electron Microscopy and Associated Techniques: Overview

X
spatial distortion due to foreshortening. The
true three-dimensional nature of the speci-
men can be recovered by applying the tech-
niques of stereomicroscopy, which invokes
the natural human visual process for stereo
imaging by combining two independent views
of the same area made with small angular dif-
ferences.
4. Other properties which can be accessed by
SEM imaging: (1) crystal structure, including
grain boundaries, crystal defects, and crystal
deformation effects (e.g., . Fig. 8); (2) mag-
netic microstructure, including magnetic
domains and interfaces; (3) applied electri-
cal fields in engineered microstructures; (4)
electron-stimulated optical emission (cath-
odoluminescence), which is sensitive to low
energy electronic structure.
Measuring the Elemental
Composition
The beam interaction with the specimen produces
two types of X-ray photon emissions which com-
pose the X-ray spectrum: (1) characteristic X-rays,
whose specific energies provide a fingerprint that
is specific to each element, with the exception of H
and He, which do not emit X-rays; and (2) con-
tinuum X-rays, which occur at all photon energies
from the measurement threshold to E
0
and form a
background beneath the characteristic X-rays.
This X-ray spectrum can be used to identify and
quantify the specific elements (excepting H and
He, which do not produce X-rays) present within
the beam-excited interaction volume, which has
dimensions ranging from approximately 100 nm
to 10 μm depending on composition and beam
energy, over a wide range of concentrations (C,
expressed in mass fraction):
“Major constituent”: 0.1 < C ≤ 1
“Minor constituent”: 0.01 ≤ C ≤ 0.1
“Trace constituent”: C < 0.01
The X-ray spectrum is measured with the semi-
conductor energy dispersive X-ray spectrometer
(EDS), which can detect photons from a threshold
of approximately 40 eV to E
0
(which can be as high
as 30 keV). Vendor software supports collection
and analysis of spectra, and these tools can be aug-
mented significantly with the open source software
National Institute of Standards and Technology
DTSA II for quantitative spectral processing and
simulation, discussed in this textbook.
Analytical software supports qualitative X-ray
microanalysis which involves assigning the char-
acteristic peaks recognized in the spectrum to
specific elements. Qualitative analysis presents
significant challenges because of mutual peak
interferences that can occur between certain
SE MAG: 500 X HV: 20.0 kV WD: 11.0 mm BSE MAG: 500 X HV: 20.0 kV WD: 11.0 mm
20 mm2 0 mm
. .Fig. 5 Topographic contrast as viewed with different detectors: Everhart–Thornley (positive bias) and semiconductor
BSE (sum mode); silver crystals; E
0
= 20 keV; Bar = 20 µm
SEM HV: 15.0 kV WD: 9.42 mm
Det: SEView field: 439 mm 100 mm
. .Fig. 6 Visualizing the third dimension. Anaglyph ste-
reo pair (red filter over left eye) of pollen grains on plant
fibers; E
0
= 15 keV; coated with Au-Pd; Bar = 100 µm
Scanning Electron Microscopy and Associated Techniques: Overview

XI
combinations of elements, for example, Ti and
Ba; S, Mo, and Pb; and many others, especially
when the peaks of major constituents interfere
with the peaks of minor or trace constituents.
Operator knowledge of the physical rules govern-
ing X-ray generation and detection is needed to
perform a careful review of software-generated
peak identifications, and this careful review must
always be performed to achieve a robust mea-
surement result.
After a successful qualitative analysis has been
performed, quantitative analysis can proceed.
The characteristic intensity for each peak is auto-
matically determined by peak fitting procedures,
such as the multiple linear least squares method.
The intensity measured for each element is pro-
portional to the concentration of that element,
but that intensity is also modified by all other ele-
ments present in the interaction volume through
their influence on the electron scattering and
retardation (“atomic number” matrix effect, Z),
X-ray absorption within the specimen (“absorp-
tion” matrix effect, A), and X-ray generation
induced by absorption of X-rays (“secondary flu-
orescence” matrix effects, F, induced by charac-
teristic X-rays and c, induced by continuum
X-rays). The complex physics of these “ZAFc”
matrix corrections has been rendered into algo-
rithms by a combined theoretical and empirical
approach. The basis of quantitative electron-
excited X-ray microanalysis is the “k-ratio proto-
col”: measurement under identical conditions
(beam energy, known electron dose, and spec-
trometer performance) of the characteristic
intensities for all elements recognized in the
unknown spectrum against a suite of standards
containing those same elements, producing a set
of k-ratios, where
kI I=
UnknownS tandard
/

(1)
for each element in the unknown. Standards are
materials of known composition that are tested to
be homogeneous at the microscopic scale, and
preferably homogeneous at the nanoscale.
Standards can be as simple as pure elements—e.g.,
C, Al, Si, Ti, Cr, Fe, Ni, Cu, Ag, Au, etc.—but for
those elements that are not stable in a vacuum
(e.g., gaseous elements such as O) or which
degrade during electron bombardment (e.g., S, P,
and Ga), stable stoichiometric compounds can be
used instead, e.g., MgO for O; FeS
2
for S; and GaP
for Ga and P. The most accurate analysis is per-
formed with standards measured on the same
instrument as the unknown(s), ideally in the same
measurement campaign, although archived
standard spectra can be effectively used if a quality
measurement program is implemented to ensure
the constancy of measurement conditions, includ-
ing spectrometer performance parameters. With
such a standards-based measurement protocol and
ZAFc matrix corrections, the accuracy of the anal-
ysis can be expressed as a relative deviation from
expected value (RDEV):
RDEV TrueMeasuredTrue%% /()[]()=´ - 100

(2)
Based on extensive testing of homogeneous
binary and multiple component compositions,
the distribution of RDEV values for major con-
stituents is such that a range of ±5 % relative cap-
tures 95 % of all analyses. The use of stable, high
integrated count spectra (>1 million total counts
from threshold to E
0
) now possible with the sili-
con drift detector EDS (SDD-EDS), enables this
level of accuracy to be achieved for major and
minor constituents even when severe peak inter-
ference occurs and there is also a large concen-
tration ratio, for example, a major constituent
interfering with a minor constituent. Trace con-
stituents that do not suffer severe interference
can be measured to limits of detection as low as
C = 0.0002 (200 parts per million) with spectra
containing >10 million counts. For interference
situations, much higher count spectra (>100
million counts) are required.
An alternative “standardless analysis” protocol
uses libraries of standard spectra (“remote stan-
dards”) measured on a different SEM platform
with a similar EDS spectrometer, ideally over a
wide range of beam energy and detector parame-
ters (resolution). These library spectra are then
adjusted to the local measurement conditions
through comparison of one or more key spectra
(e.g., locally measured spectra of particular ele-
ments such as Si and Ni). Interpolation/extrapola-
tion is used to supply estimated spectral intensities
for elements not present in or at a beam energy not
represented in the library elemental suite. Testing
of the standardless analysis method has shown
that an RDEV range of ±25 % relative is needed to
capture 95 % of all analyses.
High throughput (>100 kHz) EDS enables col-
lection of X-ray intensity maps with gray scale rep-
resentation of different concentration levels (e.g.,
. Fig. 7a). Compositional mapping by spectrum
imaging (SI) collects a full EDS spectrum at each
pixel of an x-y array, and after applying the quanti-
tative analysis procedure at each pixel, images are
created for each element where the gray (or color)
level is assigned based on the measured concentra-
tion (e.g., . Fig. 7b).
Scanning Electron Microscopy and Associated Techniques: Overview

XII
. .Fig. 7 a EDS X-ray intensity maps for Al, Fe, and Ni and color overlay; Raney nickel alloy; E
0
= 20 keV. b SEM/BSE (sum)
image and compositional maps corresponding to a
Ni Al Fe Ni
Al Fe
20µm
a
20µm
Ni Fe
wt%
BSE Al
b
BSE MAG: 1000 x HV: 20.0 kV WD: 11.0 mm
20 mm
0.001 0.01 0.1 1.0
0.1 1.01 0 100
Scanning Electron Microscopy and Associated Techniques: Overview

XIII
Measuring the Crystal Structure
An electron beam incident on a crystal can undergo
electron channeling in a shallow near-surface layer
which increases the initial beam penetration for
certain orientations of the beam relative to the
crystal planes. The additional penetration results in
a slight reduction in the electron backscattering
coefficient, which creates weak crystallographic
contrast (a few percent) in SEM images by which
differences in local crystallographic orientation
can be directly observed: grain boundaries, defor-
mations bands, and so on (e.g., . Fig. 8).
The backscattered electrons exiting the speci-
men are subject to crystallographic diffraction
effects, producing small modulations in the intensi-
ties scattered to different angles that are superim-
posed on the overall angular distribution that an
amorphous target would produce. The resulting
“electron backscatter diffraction (EBSD)” pattern
provides extensive information on the local orienta-
tion, as shown in . Fig. 8b for a crystal of hematite.
EBSD pattern angular separations provide mea-
surements of the crystal plane spacing, while the
overall EBSD pattern reveals symmetry elements.
This crystallographic information combined with
elemental analysis information obtained simultane-
ously from the same specimen region can be used to
identify the crystal structure of an unknown.
Dual-Beam Platforms: Combined
Electron and Ion Beams
A “dual-beam” instrument combines a fully func-
tional SEM with a focused ion beam (FIB), typi-
cally gallium or argon. This combination provides
a flexible platform for in situ specimen modifica-
tion through precision ion beam milling and/or
ion beam mediated material deposition with
sequential or simultaneous electron beam tech-
nique characterization of the newly revealed
specimen surfaces. Precision material removal
enables detailed study of the third dimension of a
specimen with nanoscale resolution along the
depth axis. An example of ion beam milling of a
directionally solidified Al-Cu is shown in . Fig. 9,
as imaged with the SEM column on the dual-
beam instrument. Additionally, ion-beam
induced secondary electron emission provides
scanning ion microscopy (SIM) imaging to com-
plement SEM imaging. For imaging certain speci-
men properties, such as crystallographic
structure, SIM produces stronger contrast than
SEM. There is also an important class of stand-
alone SIM instruments, such as the helium ion
microscope (HIM), that are optimized for high
resolution/high depth-of-field imaging perfor-
mance (e.g., the same area as viewed by HIM is
also shown in . Fig. 9).
a b
BSE MAG: 400 x HV: 20.0 kV WD: 11.0 mm
40 mm
. .Fig. 8 a Electron channeling contrast revealing grain boundaries in Ti-alloy (nominal composition: Ti-15Mo-3Nb-3Al-
0.2Si); E
0
= 20 keV. b Electron backscatter diffraction (EBSD) pattern from hematite at E
0
= 40 keV
Scanning Electron Microscopy and Associated Techniques: Overview

XIV
Modeling Electron and Ion
Interactions
An important component of modern Scanning
Electron Microscopy and X-ray Microanalysis
is modeling the interaction of beam electrons
and ions with the atoms of the specimen and its
environment. Such modeling supports image
interpretation, X-ray microanalysis of challeng-
ing specimens, electron crystallography methods,
and many other issues. Software tools for this pur-
pose, including Monte Carlo electron trajectory
simulation, are discussed within the text. These
tools are complemented by the extensive database
of Electron-Solid Interactions (e.g., electron scat-
tering and ionization cross sections, secondary
electron and backscattered electron coefficients,
etc.), developed by Prof. David Joy, can be found
in chapter 3 on SpringerLink: http://link.springer.
com/chapter/10.1007/978-1-4939-6676-9_3.
References
Knoll M (1935) Static potential and secondary emission of
bodies under electron radiation. Z Tech Physik 16:467
Knoll M, Theile R (1939) Scanning electron microscope for
determining the topography of surfaces and thin
layers. Z Physik 113:260
Oatley C (1972) The scanning electron microscope: part 1,
the instrument. Cambridge University Press, Cambridge
von Ardenne M (1938) The scanning electron microscope.
Theoretical fundamentals. Z Physik 109:553
magH VW DH FWcurr
3.9 mm51.2 µm
20 µm
Field of view
5.00 um
Dwell Time Mag (4x5 Polaroid)
2,540.00 X
Detector
PrimaryETDetector
50.0 us
Blankar Current
0.7 9A
Image Size
1024x1024
Working Dist
50.00 um
12.1 mm86 pA5 000 x15.00 kV
. .Fig. 9 Directionally-solidified Al-Cu eutectic alloy after ion beam milling in a dual-beam instrument, as imaged by the
SEM column (left image); same region imaged in the HIM (right image)
Scanning Electron Microscopy and Associated Techniques: Overview

XV
Contents
1 Electron Beam—Specimen Interactions: Interaction Volume�� 1
1.1 What Happens When the Beam Electrons Encounter Specimen Atoms?�� 2
1.2 Inelastic Scattering (Energy Loss) Limits Beam Electron
Travel in the Specimen�� 2
1.3 Elastic Scattering: Beam Electrons Change Direction of Flight�� 4
1.3.1 How Frequently Does Elastic Scattering Occur?�� 4
1.4 Simulating the Effects of Elastic Scattering: Monte Carlo Calculations�� 5
1.4.1 What Do Individual Monte Carlo Trajectories Look Like?�� 6
1.4.2 Monte Carlo Simulation To Visualize the Electron Interaction Volume�� 6
1.4.3 Using the Monte Carlo Electron Trajectory Simulation to Study
the Interaction Volume�� 8
1.5 A Range Equation To Estimate the Size of the Interaction Volume�� 12
References�� 14
2 Backscattered Electrons�� 15
2.1 Origin�� 16
2.1.1 The Numerical Measure of Backscattered Electrons�� 16
2.2 Critical Properties of Backscattered Electrons�� 16
2.2.1 BSE Response to Specimen Composition (η vs. Atomic Number, Z)�� 16
2.2.2 BSE Response to Specimen Inclination (η vs. Surface Tilt, θ)�� 20
2.2.3 Angular Distribution of Backscattering�� 22
2.2.4 Spatial Distribution of Backscattering�� 23
2.2.5 Energy Distribution of Backscattered Electrons�� 27
2.3 Summary�� 27
References�� 28
3 Secondary Electrons�� 29
3.1 Origin�� 30
3.2 Energy Distribution�� 30
3.3 Escape Depth of Secondary Electrons�� 30
3.4 Secondary Electron Yield Versus Atomic Number�� 30
3.5 Secondary Electron Yield Versus Specimen Tilt�� 34
3.6 Angular Distribution of Secondary Electrons�� 34
3.7 Secondary Electron Yield Versus Beam Energy�� 35
3.8 Spatial Characteristics of Secondary Electrons�� 35
References�� 37
4 X-Rays�� 39
4.1 Overview�� 40
4.2 Characteristic X-Rays�� 40
4.2.1 Origin�� 40
4.2.2 Fluorescence Yield�� 41
4.2.3 X-Ray Families�� 42
4.2.4 X-Ray Nomenclature�� 43
4.2.5 X-Ray Weights of Lines�� 44
4.2.6 Characteristic X-Ray Intensity�� 44
4.3 X-Ray Continuum (bremsstrahlung)�� 47
4.3.1 X-Ray Continuum Intensity�� 49
4.3.2 The Electron-Excited X-Ray Spectrum, As-Generated�� 49
4.3.3 Range of X-ray Production�� 50
4.3.4 Monte Carlo Simulation of X-Ray Generation�� 51
4.3.5 X-ray Depth Distribution Function, ϕ(ρz)�� 53

XVI
4.4 X-Ray Absorption�� 54
4.5 X-Ray Fluorescence�� 59
References�� 63
5 Scanning Electron Microscope (SEM) Instrumentation�� 65
5.1 Electron Beam Parameters�� 66
5.2 Electron Optical Parameters�� 66
5.2.1 Beam Energy�� 66
5.2.2 Beam Diameter�� 67
5.2.3 Beam Current�� 67
5.2.4 Beam Current Density�� 68
5.2.5 Beam Convergence Angle, α�� 68
5.2.6 Beam Solid Angle�� 69
5.2.7 Electron Optical Brightness, β�� 70
5.2.8 Focus�� 71
5.3 SEM Imaging Modes�� 75
5.3.1 High Depth-of-Field Mode�� 75
5.3.2 High-Current Mode�� 78
5.3.3 Resolution Mode�� 80
5.3.4 Low-Voltage Mode�� 81
5.4 Electron Detectors�� 83
5.4.1 Important Properties of BSE and SE for Detector Design and Operation�� 83
5.4.2 Detector Characteristics�� 83
5.4.3 Common Types of Electron Detectors�� 85
5.4.4 Secondary Electron Detectors�� 86
5.4.5 Specimen Current: The Specimen as Its Own Detector�� 88
5.4.6 A Useful, Practical Measure of a Detector: Detective
Quantum Efficiency�� 89
References�� 91
6 Image Formation�� 93
6.1 Image Construction by Scanning Action�� 94
6.2 Magnification�� 95
6.2.1 Magnification, Image Dimensions, and Scale Bars�� 95
6.3 Making Dimensional Measurements With the SEM:
How Big Is That Feature?�� 95
6.3.1 Calibrating the Image�� 95
6.4 Image Defects�� 98
6.4.1 Projection Distortion (Foreshortening)�� 98
6.4.2 Image Defocusing (Blurring)�� 100
6.5 Making Measurements on Surfaces With Arbitrary Topography:
Stereomicroscopy�� 102
6.5.1 Qualitative Stereomicroscopy�� 103
6.5.2 Quantitative Stereomicroscopy�� 107
References�� 110
7 SEM Image Interpretation�� 111
7.1 Information in SEM Images�� 112
7.2 Interpretation of SEM Images of Compositional Microstructure�� 112
7.2.1 Atomic Number Contrast With Backscattered Electrons�� 112
7.2.2 Calculating Atomic Number Contrast�� 113
7.2.3 BSE Atomic Number Contrast With the Everhart–Thornley Detector�� 113
7.3 Interpretation of SEM Images of Specimen Topography�� 114
7.3.1 Imaging Specimen Topography With the Everhart–Thornley Detector�� 115
7.3.2 The Light-Optical Analogy to the SEM/E–T (Positive Bias) Image�� 116
7.3.3 Imaging Specimen Topography With a Semiconductor BSE Detector�� 119
References�� 121
Contents

XVII
8 The Visibility of Features in SEM Images�� 123
8.1 Signal Quality: Threshold Contrast and Threshold Current�� 124
References�� 131
9 Image Defects�� 133
9.1 Charging�� 134
9.1.1 What Is Specimen Charging?�� 134
9.1.2 Recognizing Charging Phenomena in SEM Images�� 135
9.1.3 Techniques to Control Charging Artifacts (High Vacuum Instruments)�� 139
9.2 Radiation Damage�� 142
9.3 Contamination�� 143
9.4 Moiré Effects: Imaging What Isn’t Actually There�� 144
References�� 146
10 High Resolution Imaging�� 147
10.1 What Is “High Resolution SEM Imaging”?�� 148
10.2 Instrumentation Considerations�� 148
10.3 Pixel Size, Beam Footprint, and Delocalized Signals�� 148
10.4 Secondary Electron Contrast at High Spatial Resolution�� 150
10.4.1 SE range Effects Produce Bright Edges (Isolated Edges)�� 151
10.4.2 Even More Localized Signal: Edges Which Are Thin Relative
to the Beam Range�� 152
10.4.3 Too Much of a Good Thing: The Bright Edge Effect Can Hinder
Distinguishing Shape�� 153
10.4.4 Too Much of a Good Thing: The Bright Edge Effect Hinders
Locating the True Position of an Edge for Critical Dimension Metrology�� 154
10.5 Achieving High Resolution with Secondary Electrons�� 156
10.5.1 Beam Energy Strategies�� 156
10.5.2 Improving the SE
1
Signal�� 158
10.5.3 Eliminate the Use of SEs Altogether: “Low Loss BSEs“�� 161
10.6 Factors That Hinder Achieving High Resolution�� 163
10.6.1 Achieving Visibility: The Threshold Contrast�� 163
10.6.2 Pathological Specimen Behavior�� 163
10.6.3 Pathological Specimen and Instrumentation Behavior�� 164
References�� 164
11 Low Beam Energy SEM�� 165
11.1 What Constitutes “Low” Beam Energy SEM Imaging?�� 166
11.2 Secondary Electron and Backscattered Electron Signal Characteristics
in the Low Beam Energy Range�� 166
11.3 Selecting the Beam Energy to Control the Spatial Sampling
of Imaging Signals�� 169
11.3.1 Low Beam Energy for High Lateral Resolution SEM�� 169
11.3.2 Low Beam Energy for High Depth Resolution SEM�� 169
11.3.3 Extremely Low Beam Energy Imaging�� 171
References�� 172
12 Variable Pressure Scanning Electron Microscopy (VPSEM)�� 173
12.1 Review: The Conventional SEM High Vacuum Environment�� 174
12.1.1 Stable Electron Source Operation�� 174
12.1.2 Maintaining Beam Integrity�� 174
12.1.3 Stable Operation of the Everhart–Thornley Secondary Electron Detector�� 174
12.1.4 Minimizing Contamination�� 174
12.2 How Does VPSEM Differ From the Conventional SEM
Vacuum Environment?�� 174
Contents

XVIII
12.3 Benefits of Scanning Electron Microscopy at Elevated Pressures�� 175
12.3.1 Control of Specimen Charging�� 175
12.3.2 Controlling the Water Environment of a Specimen�� 176
12.4 Gas Scattering Modification of the Focused Electron Beam�� 177
12.5 VPSEM Image Resolution�� 181
12.6 Detectors for Elevated Pressure Microscopy�� 182
12.6.1 Backscattered Electrons—Passive Scintillator Detector�� 182
12.6.2 Secondary Electrons–Gas Amplification Detector�� 182
12.7 Contrast in VPSEM�� 184
References�� 185
13 ImageJ and Fiji�� 187
13.1 The ImageJ Universe�� 188
13.2 Fiji�� 188
13.3 Plugins�� 190
13.4 Where to Learn More�� 191
References�� 193
14 SEM Imaging Checklist�� 195
14.1 Specimen Considerations (High Vacuum SEM; Specimen Chamber Pressure < 10
−3
Pa)�� 197
14.1.1 Conducting or Semiconducting Specimens�� 197
14.1.2 Insulating Specimens�� 197
14.2 Electron Signals Available�� 197
14.2.1 Beam Electron Range�� 197
14.2.2 Backscattered Electrons �� 197
14.2.3 Secondary Electrons �� 197
14.3 Selecting the Electron Detector�� 198
14.3.1 Everhart–Thornley Detector (“Secondary Electron” Detector)�� 198
14.3.2 Backscattered Electron Detectors�� 198
14.3.3 “Through-the-Lens” Detectors�� 198
14.4 Selecting the Beam Energy for SEM Imaging�� 198
14.4.1 Compositional Contrast With Backscattered Electrons�� 198
14.4.2 Topographic Contrast With Backscattered Electrons�� 198
14.4.3 Topographic Contrast With Secondary Electrons�� 198
14.4.4 High Resolution SEM Imaging�� 198
14.5 Selecting the Beam Current�� 199
14.5.1 High Resolution Imaging�� 199
14.5.2 Low Contrast Features Require High Beam Current and/or Long Frame Time to Establish Visibility�� 199
14.6 Image Presentation�� 199
14.6.1 “Live” Display Adjustments�� 199
14.6.2 Post-Collection Processing�� 199
14.7 Image Interpretation�� 199
14.7.1 Observer’s Point of View�� 199
14.7.2 Direction of Illumination�� 199
14.7.3 Contrast Encoding�� 200
14.7.4 Imaging Topography With the Everhart–Thornley Detector�� 200
14.7.5 Annular BSE Detector (Semiconductor Sum Mode A + B and Passive Scintillator)�� 200
14.7.6 Semiconductor BSE Detector Difference Mode, A−B�� 200
14.7.7 Everhart–Thornley Detector, Negatively Biased to Reject SE�� 200
14.8 Variable Pressure Scanning Electron Microscopy (VPSEM)�� 200
14.8.1 VPSEM Advantages�� 200
14.8.2 VPSEM Disadvantages�� 200
15 SEM Case Studies�� 201
15.1 Case Study: How High Is That Feature Relative to Another?�� 202
15.2 Revealing Shallow Surface Relief�� 204
15.3 Case Study: Detecting Ink-Jet Printer Deposits�� 206
Contents

XIX
16 Energy Dispersive X-ray Spectrometry: Physical Principles and User-Selected
Parameters�� 209
16.1 The Energy Dispersive Spectrometry (EDS) Process�� 210
16.1.1 The Principal EDS Artifact: Peak Broadening (EDS Resolution Function)�� 210
16.1.2 Minor Artifacts: The Si-Escape Peak�� 213
16.1.3 Minor Artifacts: Coincidence Peaks�� 213
16.1.4 Minor Artifacts: Si Absorption Edge and Si Internal Fluorescence Peak�� 215
16.2 “Best Practices” for Electron-Excited EDS Operation�� 216
16.2.1 Operation of the EDS System�� 216
16.3 Practical Aspects of Ensuring EDS Performance for a Quality
Measurement Environment�� 219
16.3.1 Detector Geometry�� 219
16.3.2 Process Time�� 222
16.3.3 Optimal Working Distance�� 222
16.3.4 Detector Orientation�� 223
16.3.5 Count Rate Linearity�� 225
16.3.6 Energy Calibration Linearity�� 226
16.3.7 Other Items�� 227
16.3.8 Setting Up a Quality Control Program�� 228
16.3.9 Purchasing an SDD�� 230
References�� 234
17 DTSA-II EDS Software�� 235
17.1 Getting Started With NIST DTSA-II�� 236
17.1.1 Motivation�� 236
17.1.2 Platform�� 236
17.1.3 Overview�� 236
17.1.4 Design�� 237
17.1.5 The Three -Leg Stool: Simulation, Quantification and Experiment Design�� 237
17.1.6 Introduction to Fundamental Concepts�� 238
17.2 Simulation in DTSA-II�� 245
17.2.1 Introduction�� 245
17.2.2 Monte Carlo Simulation�� 245
17.2.3 Using the GUI To Perform a Simulation�� 247
17.2.4 Optional Tables�� 262
References�� 264
18 Qualitative Elemental Analysis by Energy Dispersive X-Ray Spectrometry�� 265
18.1 Quality Assurance Issues for Qualitative Analysis: EDS Calibration�� 266
18.2 Principles of Qualitative EDS Analysis�� 266
18.2.1 Critical Concepts From the Physics of Characteristic X-ray Generation
and Propagation�� 266
18.2.2 X-Ray Energy Database: Families of X-Rays�� 269
18.2.3 Artifacts of the EDS Detection Process�� 269
18.3 Performing Manual Qualitative Analysis�� 275
18.3.1 Why are Skills in Manual Qualitative Analysis Important?�� 275
18.3.2 Performing Manual Qualitative Analysis: Choosing the Instrument
Operating Conditions�� 277
18.4 Identifying the Peaks�� 278
18.4.1 Employ the Available Software Tools�� 278
18.4.2 Identifying the Peaks: Major Constituents�� 280
18.4.3 Lower Photon Energy Region�� 281
18.4.4 Identifying the Peaks: Minor and Trace Constituents�� 281
18.4.5 Checking Your Work�� 281
18.5 A Worked Example of Manual Peak Identification�� 281
References�� 287
Contents

XX
19 Quantitative Analysis: From k-ratio to Composition�� 289
19.1 What Is a k-ratio?�� 290
19.2 Uncertainties in k-ratios�� 291
19.3 Sets of k-ratios�� 291
19.4 Converting Sets of k-ratios Into Composition�� 292
19.5 The Analytical Total�� 292
19.6 Normalization�� 292
19.7 Other Ways to Estimate C
Z
�� 293
19.7.1 Oxygen by Assumed Stoichiometry�� 293
19.7.2 Waters of Crystallization�� 293
19.7.3 Element by Difference�� 293
19.8 Ways of Reporting Composition�� 294
19.8.1 Mass Fraction�� 294
19.8.2 Atomic Fraction�� 294
19.8.3 Stoichiometry�� 294
19.8.4 Oxide Fractions�� 294
19.9 The Accuracy of Quantitative Electron-Excited X-ray Microanalysis�� 295
19.9.1 Standards-Based k-ratio Protocol�� 295
19.9.2 “Standardless Analysis”�� 296
19.10 Appendix�� 298
19.10.1 The Need for Matrix Corrections To Achieve Quantitative Analysis�� 298
19.10.2 The Physical Origin of Matrix Effects�� 299
19.10.3 ZAF Factors in Microanalysis�� 299
References�� 307
20 Quantitative Analysis: The SEM/EDS Elemental Microanalysis k-ratio
Procedure for Bulk Specimens, Step-by-Step�� 309
20.1 Requirements Imposed on the Specimen and Standards�� 311
20.2 Instrumentation Requirements�� 311
20.2.1 Choosing the EDS Parameters�� 311
20.2.2 Choosing the Beam Energy, E
0
�� 313
20.2.3 Measuring the Beam Current�� 313
20.2.4 Choosing the Beam Current�� 314
20.3 Examples of the k-ratio/Matrix Correction Protocol with DTSA II�� 316
20.3.1 Analysis of Major Constituents (C > 0.1 Mass Fraction)
with Well-Resolved Peaks�� 316
20.3.2 Analysis of Major Constituents (C > 0.1 Mass Fraction)
with Severely Overlapping Peaks�� 318
20.3.3 Analysis of a Minor Constituent with Peak Overlap From
a Major Constituent�� 319
20.3.4 Ba-Ti Interference in BaTiSi
3
O
9
�� 319
20.3.5 Ba-Ti Interference: Major/Minor Constituent Interference in K2496
Microanalysis Glass�� 319
20.4 The Need for an Iterative Qualitative and Quantitative
Analysis Strategy�� 319
20.4.1 Analysis of a Complex Metal Alloy, IN100�� 320
20.4.2 Analysis of a Stainless Steel�� 323
20.4.3 Progressive Discovery: Repeated Qualitative–Quantitative Analysis
Sequences�� 324
20.5 Is the Specimen Homogeneous?�� 326
20.6 Beam-Sensitive Specimens�� 331
20.6.1 Alkali Element Migration�� 331
20.6.2 Materials Subject to Mass Loss During Electron Bombardment—
the Marshall-Hall Method�� 334
References�� 339
Contents

XXI
21 Trace Analysis by SEM/EDS�� 341
21.1 Limits of Detection for SEM/EDS Microanalysis�� 342
21.2 Estimating the Concentration Limit of Detection, C
DL
�� 343
21.2.1 Estimating C
DL
from a Trace or Minor Constituent from Measuring
a Known Standard�� 343
21.2.2 Estimating C
DL
After Determination of a Minor or Trace Constituent
with Severe Peak Interference from a Major Constituent�� 343
21.2.3 Estimating C
DL
When a Reference Value for Trace or
Minor Element Is Not Available�� 343
21.3 Measurements of Trace Constituents by Electron-Excited Energy
Dispersive X-ray Spectrometry�� 345
21.3.1 Is a Given Trace Level Measurement Actually Valid?�� 345
21.4 Pathological Electron Scattering Can Produce “Trace” Contributions
to EDS Spectra�� 350
21.4.1 Instrumental Sources of Trace Analysis Artifacts�� 350
21.4.2 Assessing Remote Excitation Sources in an SEM-EDS System�� 353
21.5 Summary�� 357
References�� 357
22 Low Beam Energy X-Ray Microanalysis�� 359
22.1 What Constitutes “Low” Beam Energy X-Ray Microanalysis?�� 360
22.1.1 Characteristic X-ray Peak Selection Strategy for Analysis�� 364
22.1.2 Low Beam Energy Analysis Range�� 364
22.2 Advantage of Low Beam Energy X-Ray Microanalysis�� 365
22.2.1 Improved Spatial Resolution�� 365
22.2.2 Reduced Matrix Absorption Correction�� 366
22.2.3 Accurate Analysis of Low Atomic Number Elements at Low Beam Energy�� 366
22.3 Challenges and Limitations of Low Beam Energy X-Ray Microanalysis�� 369
22.3.1 Reduced Access to Elements�� 369
22.3.2 Relative Depth of X-Ray Generation: Susceptibility to Vertical Heterogeneity�� 372
22.3.3 At Low Beam Energy, Almost Everything Is Found To Be Layered�� 373
References�� 380
23 Analysis of Specimens with Special Geometry: Irregular Bulk
Objects and Particles�� 381
23.1 The Origins of “Geometric Effects”: Bulk Specimens�� 382
23.2 What Degree of Surface Finish Is Required for Electron-Excited X-ray
Microanalysis To Minimize Geometric Effects?�� 384
23.2.1 No Chemical Etching�� 384
23.3 Consequences of Attempting Analysis of Bulk Materials
With Rough Surfaces�� 385
23.4 Useful Indicators of Geometric Factors Impact on Analysis�� 386
23.4.1 The Raw Analytical Total�� 386
23.4.2 The Shape of the EDS Spectrum�� 389
23.5 Best Practices for Analysis of Rough Bulk Samples�� 391
23.6 Particle Analysis�� 394
23.6.1 How Do X-ray Measurements of Particles Differ
From Bulk Measurements?�� 394
23.6.2 Collecting Optimum Spectra From Particles�� 395
23.6.3 X-ray Spectrum Imaging: Understanding Heterogeneous Materials�� 400
23.6.4 Particle Geometry Factors Influencing Quantitative Analysis of Particles�� 403
23.6.5 Uncertainty in Quantitative Analysis of Particles�� 405
23.6.6 Peak-to-Background (P/B) Method�� 408
23.7 Summary�� 410
References�� 411
Contents

XXII
24 Compositional Mapping�� 413
24.1 Total Intensity Region-of-Interest Mapping�� 414
24.1.1 Limitations of Total Intensity Mapping�� 415
24.2 X-Ray Spectrum Imaging�� 417
24.2.1 Utilizing XSI Datacubes�� 419
24.2.2 Derived Spectra�� 419
24.3 Quantitative Compositional Mapping�� 424
24.4 Strategy for XSI Elemental Mapping Data Collection�� 430
24.4.1 Choosing the EDS Dead-Time�� 430
24.4.2 Choosing the Pixel Density�� 432
24.4.3 Choosing the Pixel Dwell Time�� 434
References�� 439
25 Attempting Electron-Excited X-Ray Microanalysis in the Variable Pressure
Scanning Electron Microscope (VPSEM)�� 441
25.1 Gas Scattering Effects in the VPSEM�� 442
25.1.1 Why Doesn’t the EDS Collimator Exclude the Remote Skirt X-Rays?�� 446
25.1.2 Other Artifacts Observed in VPSEM X-Ray Spectrometry�� 448
25.2 What Can Be Done To Minimize gas Scattering in VPSEM?�� 450
25.2.1 Workarounds To Solve Practical Problems�� 451
25.2.2 Favorable Sample Characteristics�� 451
25.2.3 Unfavorable Sample Characteristics�� 456
References�� 459
26 Energy Dispersive X-Ray Microanalysis Checklist�� 461
26.1 Instrumentation�� 462
26.1.1 SEM�� 462
26.1.2 EDS Detector�� 462
26.1.3 Probe Current Measurement Device�� 462
26.1.4 Conductive Coating�� 463
26.2 Sample Preparation�� 463
26.2.1 Standard Materials�� 464
26.2.2 Peak Reference Materials�� 464
26.3 Initial Set-Up�� 464
26.3.1 Calibrating the EDS Detector�� 464
26.4 Collecting Data�� 466
26.4.1 Exploratory Spectrum�� 466
26.4.2 Experiment Optimization�� 467
26.4.3 Selecting Standards�� 467
26.4.4 Reference Spectra�� 467
26.4.5 Collecting Standards�� 467
26.4.6 Collecting Peak-Fitting References�� 467
26.4.7 Collecting Spectra From the Unknown�� 467
26.5 Data Analysis�� 468
26.5.1 Organizing the Data�� 468
26.5.2 Quantification�� 468
26.6 Quality Check�� 468
26.6.1 Check the Residual Spectrum After Peak Fitting�� 468
26.6.2 Check the Analytic Total�� 469
26.6.3 Intercompare the Measurements�� 469
Reference�� 470
27 X-Ray Microanalysis Case Studies�� 471
27.1 Case Study: Characterization of a Hard-Facing Alloy Bearing Surface�� 472
27.2 Case Study: Aluminum Wire Failures in Residential Wiring�� 474
27.3 Case Study: Characterizing the Microstructure of a Manganese Nodule�� 476
References�� 479
Contents

XXIII
28 Cathodoluminescence�� 481
28.1 Origin�� 482
28.2 Measuring Cathodoluminescence�� 483
28.2.1 Collection of CL�� 483
28.2.2 Detection of CL�� 483
28.3 Applications of CL�� 485
28.3.1 Geology�� 485
28.3.2 Materials Science�� 485
28.3.3 Organic Compounds�� 489
References�� 489
29 Characterizing Crystalline Materials in the SEM�� 491
29.1 Imaging Crystalline Materials with Electron Channeling Contrast�� 492
29.1.1 Single Crystals�� 492
29.1.2 Polycrystalline Materials�� 494
29.1.3 Conditions for Detecting Electron Channeling Contrast�� 496
29.2 Electron Backscatter Diffraction in the Scanning Electron
Microscope�� 496
29.2.1 Origin of EBSD Patterns�� 498
29.2.2 Cameras for EBSD Pattern Detection�� 499
29.2.3 EBSD Spatial Resolution�� 499
29.2.4 How Does a Modern EBSD System Index Patterns�� 501
29.2.5 Steps in Typical EBSD Measurements�� 502
29.2.6 Display of the Acquired Data�� 505
29.2.7 Other Map Components�� 508
29.2.8 Dangers and Practice of “Cleaning” EBSD Data�� 508
29.2.9 Transmission Kikuchi Diffraction in the SEM�� 509
29.2.10 Application Example�� 510
29.2.11 Summary�� 513
29.2.12 Electron Backscatter Diffraction Checklist�� 513
References�� 514
30 Focused Ion Beam Applications in the SEM Laboratory�� 517
30.1 Introduction�� 518
30.2 Ion–Solid Interactions�� 518
30.3 Focused Ion Beam Systems�� 519
30.4 Imaging with Ions�� 520
30.5 Preparation of Samples for SEM�� 521
30.5.1 Cross-Section Preparation�� 522
30.5.2 FIB Sample Preparation for 3D Techniques and Imaging�� 524
30.6 Summary�� 526
References�� 528
31 Ion Beam Microscopy�� 529
31.1 What Is So Useful About Ions?�� 530
31.2 Generating Ion Beams�� 533
31.3 Signal Generation in the HIM�� 534
31.4 Current Generation and Data Collection in the HIM�� 536
31.5 Patterning with Ion Beams�� 537
31.6 Operating the HIM�� 538
31.7 Chemical Microanalysis with Ion Beams�� 538
References�� 539
Supplementary Information�� 541
Appendix�� 542
Index�� 547
Contents

© Springer Science+Business Media LLC 2018
J. Goldstein et al., Scanning Electron Microscopy and X-Ray Microanalysis,
https://doi.org/10.1007/978-1-4939-6676-9_1
1
Electron Beam—Specimen
Interactions: Interaction
Volume
1
1.1 What Happens When the Beam Electrons Encounter
Specimen Atoms? – 2
1.2 Inelastic Scattering (Energy Loss) Limits Beam
Electron Travel in the Specimen – 2
1.3 Elastic Scattering: Beam Electrons Change
Direction of Flight – 4
1.3.1 How Frequently Does Elastic Scattering Occur? – 4
1.4 Simulating the Effects of Elastic Scattering:
Monte Carlo Calculations – 5
1.4.1 What Do Individual Monte Carlo Trajectories Look Like? – 6
1.4.2 Monte Carlo Simulation To Visualize the Electron
Interaction Volume – 6
1.4.3 Using the Monte Carlo Electron Trajectory Simulation to Study
the Interaction Volume – 8
1.5 A Range Equation To Estimate the Size of the Interaction
Volume – 12
References – 14

2
1
1.1 What Happens When the Beam
Electrons Encounter Specimen Atoms?
By selecting the operating parameters of the SEM electron
gun, lenses, and apertures, the microscopist controls the
characteristics of the focused beam that reaches the speci-
men surface: energy (typically selected in the range 0.1–
30 keV), diameter (0.5 nm to 1 μm or larger), beam current
(1 pA to 1 μA), and convergence angle (semi-cone angle
0.001–0.05 rad). In a conventional high vacuum SEM (typi-
cally with the column and specimen chamber pressures
reduced below 10
−3
Pa), the residual atom density is so low
that the beam electrons are statistically unlikely to encounter
any atoms of the residual gas along the flight path from the
electron source to the specimen, a distance of approximately
25 cm.
kThe initial dimensional scale
With a cold or thermal field emission gun on a high-
performance SEM, the incident beam can be focused to 1 nm
in diameter, which means that for a target such as gold (atom
diameter ~ 288 pm), there are approximately 12 gold atoms in
the first atomic layer of the solid within the area of the beam
footprint at the surface.
At the specimen surface the atom density changes
abruptly to the very high density of the solid. The beam elec-
trons interact with the specimen atoms through a variety of
physical processes collectively referred to as “scattering
events.” The overall effects of these scattering events are to
transfer energy to the specimen atoms from the beam elec-
trons, thus setting a limit on their travel within the solid, and
to alter the direction of travel of the beam electrons away
from the well-defined incident beam trajectory. These beam
electron–specimen interactions produce the backscattered
electrons (BSE), secondary electrons (SE), and X-rays that
convey information about the specimen, such as coarse- and
fine-scale topographic features, composition, crystal struc-
ture, and local electrical and magnetic fields. At the level
needed to interpret SEM images and to perform electron-
excited X-ray microanalysis, the complex variety of scatter-
ing processes will be broadly classified into “inelastic” and
“elastic” scattering.
1.2 Inelastic Scattering (Energy Loss)
Limits Beam Electron Travel
in the Specimen
“Inelastic” scattering refers to a variety of physical processes
that act to progressively reduce the energy of the beam elec-
tron by transferring that energy to the specimen atoms
through interactions with tightly bound inner-shell atomic
electrons and loosely bound valence electrons. These energy
loss processes include ejection of weakly bound outer-shell
atomic electrons (binding energy of a few eV) to form sec-
ondary electrons; ejection of tightly bound inner shell atomic
electrons (binding energy of hundreds to thousands of eV)
which subsequently results in emission of characteristic
X-rays; deceleration of the beam electron in the electrical
field of the atoms producing an X-ray continuum over all
energies from a few eV up to the beam’s landing energy (E
0
)
(bremsstrahlung or “braking radiation”); generation of waves
in the free electron gas that permeates conducting metallic
solids (plasmons); and heating of the specimen (phonon pro-
duction). While energy is lost in these inelastic scattering
events, the beam electrons only deviate slightly from their
current path. The energy loss due to inelastic scattering sets
an eventual limit on how far the beam electron can travel in
the specimen before it loses all of its energy and is absorbed
by the specimen.
To understand the specific limitations on the distance
traveled in the specimen imposed by inelastic scattering, a
mathematical description is needed of the rate of energy loss
(incremental dE, measured in eV) with distance (incremen-
tal ds, measured in nm) traveled in the specimen. Although
the various inelastic scattering energy loss processes are
discrete and independent, Bethe (1930) was able to sum-
marize their collective effects into a “continuous energy loss
approximation”:
dd eVnmEs ZAEE J// ./ ln./() =− () ()7851 166ρ

(1.1a)
where E is the beam energy (keV), Z is the atomic number, ρ
is the density (g/cm
3
), A is the atomic weight (g/mol), and J is
the “mean ionization potential” (keV) given by
JZ ZkeVx()=+()
−−
976585 10
0193
..
.

(1.1b)
The Bethe expression is plotted for several elements (C, Al,
Cu, Ag, Au) over the range of “conventional” SEM operat-
ing energies, 5–30 keV in . Fig. 1.1. This figure reveals that
the rate of energy loss dE/ds increases as the electron
energy decreases and increases with the atomic number of
the target. An electron with a beam energy of 20 keV loses
energy at approximately 10 eV/nm in Au, so that if this rate
was constant, the total path traveled in the specimen would
be approximately 20,000 eV/(10 eV/nm) = 2000 nm = 2 μm.
A better estimate of this electron “Bethe range” can be
made by explicitly considering the energy dependence of
dE/ds through integration of the Bethe expression, Eq. 1.1a,
from the incident energy down to a lower cut-off energy
(typically ~ 2 keV due to limitations on the range of appli-
cability of the Bethe expression; see further discussion
below). Based on this calculation, the Bethe range for the
selection of elements is shown in . Fig. 1.2. At a particular
incident beam energy, the Bethe range decreases as the
atomic number of the target increases, while for a particu-
lar target, the Bethe range increases as the incident beam
energy increases.
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

3 1
kNote the change of scale
The Bethe range for Au with an incident beam energy of
20 keV is approximately 1200 nm, a linear change in scale of
a factor of 1200 over an incident beam diameter of 1 nm. If
the beam–specimen interactions were restricted to a cylin-
drical column with the circular beam entrance footprint as its
cross section and the Bethe range as its altitude, the volume
of a cylinder 1 nm in diameter and 1200 nm deep would be
approximately 940 nm
3
, and the number of gold atoms it
contained would be approximately 7.5 × 10
4
, which can be
compared to the incident beam footprint surface atom count
of approximately 12.
25
Au
Cu
C
Ag
Al
15
15 25
5
5
0
20
10
10 20
Incident beam energy (keV)
Energy loss rate (eV/nm)
Bethe continuous energy loss model
30
. .Fig. 1.1 Bethe continuous
energy loss model calculations for
dE/ds in C, Al, Cu, Ag, and Au as a
function of electron energy
14000
12000
10000
8000
6000
4000
2000
0
51 02 0
Incident beam energy (keV)
Bethe range (nm)
Bethe range
C
Al
Au
Cu, Ag
3015 25
. .Fig. 1.2 Bethe range calcula-
tion from the continuous energy
loss model by integrating over the
range of energy from E
0
down to a
cut-off energy of 2 keV
1.2 · Inelastic Scattering (Energy Loss) Limits Beam Electron Travel in the Specimen

4
1
1.3 Elastic Scattering: Beam Electrons
Change Direction of Flight
Simultaneously with inelastic scattering, “elastic scattering”
events occur when the beam electron is deflected by the elec-
trical field of an atom (the positive nuclear charge as partially
shielded by the negative charge of the atom’s orbital elec-
trons), causing the beam electron to deviate from its previous
path onto a new trajectory, as illustrated schematically in
. Fig. 1.3a. The probability of elastic scattering depends
strongly on the nuclear charge (atomic number Z) and the
energy of the electron, E (keV) and is expressed mathemati-
cally as a cross section, Q:
QZ E
elastic
events electr
()
./ cot/
[/
>
−
=× () ()
>
φ
φ
φ
0
162102
2022 2
0
0
oonatomcm/
2
()





(1.2)
where ϕ
0
is a threshold elastic scattering angle, for example,
2°. Despite the angular deviation, the beam electron energy is
effectively unchanged in energy. While the average elastic
scattering event causes an angular change of only a few
degrees, deviations up to 180
o
are possible in a single elastic
scattering event. Elastic scattering causes beam electrons to
deviate out of the narrow angular range of incident trajecto-
ries defined by the convergence of the incident beam as con-
trolled by the electron optics.
1.3.1 How Frequently Does Elastic
Scattering Occur?
The elastic scattering cross section, Eq. 1.2, can be used to
estimate how far the beam electron must travel on average to
experience an elastic scattering event, a distance called the
“mean free path,” λ:
λρ
φelastic elastic
cm()=



>
AN Q/
()0
0

(1.3a)
λρ
φelastic elastic
nm()= 



>
10
7
0
0
AN Q/
()

(1.3b)
where A is the atomic weight (g/mol), N
0
is Avogadro’s num-
ber (atoms/mol), and ρ is the density (g/cm
3
). . Figure 1.4
shows a plot of λ
elastic
for various elements as a function of
electron energy, where it can be seen that the mean free path
is of the order of nm. Elastic scattering is thus likely to occur
hundreds to thousands of times along a Bethe range of sev-
eral hundred to several thousand nanometers.
P1
P1
P1
P2
P3
a
b
c
. .Fig. 1.3 a Schematic illustration of elastic scattering. An energetic
electron is deflected by the electrical field of an atom at location P1
through an angle ϕ
elastic
. b Schematic illustration of the elastic scatter-
ing cone. The energetic electron scatters elastically at point P1 and can
land at any location on the circumference of the base of the cone with
equal probability. c Schematic illustration of a second scattering step,
carrying the energetic electron from point P2 to point P3
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

5 1
1.4 Simulating the Effects of Elastic
Scattering: Monte Carlo Calculations
Inelastic scattering sets a limit on the total distance traveled
by the beam electron. The Bethe range is an estimate of this
distance and can be found by integrating the Bethe continu-
ous energy loss expression from the incident beam energy E
0

down to a low energy limit, for example, 2 keV. Estimating
the effects of elastic scattering on the beam electrons is much
more complicated. Any individual elastic scattering event
can result in a scattering angle within a broad range from a
threshold of a fraction of a degree up to 180°, with small scat-
tering angles much more likely than very large values and an
average value typically in the range 5–10°. Moreover, the
electron scattered by the atom through an angle ϕ in
. Fig. 1.3a at point P1 can actually follow any path along the
surface of the three-dimensional scattering cone shown in
. Fig. 1.3b and can land anywhere in the circumference of
the base of the scattering cone (i.e., the azimuthal angle in
the base of the cone ranges from 0 to 360° with equal proba-
bility), resulting in a three-dimensional path. The length of
the trajectory along the surface of the scattering cone
depends on the frequency of elastic events with distance
traveled and can be estimated from Eq. 1.3a for the elastic
scattering mean free path, λ
elastic
. The next elastic scattering
event P2 causes the electron to deviate in a new direction, as
shown in . Fig. 1.3c, creating an increasingly complex path.
Because of the random component of scattering at each of
many steps, this complex behavior cannot be adequately
described by an algebraic expression like the Bethe continu-
ous energy loss equation. Instead, a stepwise simulation of
the electron's behavior must be constructed that incorpo-
rates inelastic and elastic scattering. Several simplifications
are introduced to create a practical “Monte Carlo electron
trajectory simulation”:
1. All of the angular deviation of the beam electron is ascribed
to elastic scattering. A mathematical model for elastic
scattering is applied that utilizes a random number (hence
the name “Monte Carlo” from the supposed randomness of
gambling) to select a properly weighted value of the elastic
scattering angle out of the possible range (from a threshold
value of approximately 1° to a maximum of 180°). A second
random number is used to select the azimuthal angle in the
base of the scattering cone in . Fig. 1.1c.
2. The distance between elastic scattering events, s, which
lies on the surface of the scattering cone in . Fig. 1.3b, is
calculated from the elastic mean free path, Eq. 1.3b.
3. Inelastic scattering is calculated with the Bethe
continuous energy loss expression, Eq. 1.1b. The specific
energy loss, ΔE, along the path, s, in the surface of the
scattering cone, . Fig. 1.3b, is calculated with the Bethe
continuous energy loss expression: ΔE = (dE/ds)*s
Elastic scattering mean free path (f
0
= 2°)
10
0.1
0.01
1
51 02 0
Beam energy (keV)
Elastic mean free path (nm)
3015
C
Al
Ag
Au
Cu
25
. .Fig. 1.4 Elastic mean free path
as a function of electron kinetic
energy for various elements
1.4 · Simulating the Effects of Elastic Scattering: Monte Carlo Calculations

6
1
Given a specific set of these parameters, the Monte Carlo elec-
tron trajectory simulation utilizes geometrical expressions to
calculate the successive series of locations P1, P2, P3, etc., suc-
cessively determining the coordinate locations (x, y, z) that the
energetic electron follows within the solid. At each location P,
the newly depreciated energy of the electron is known, and after
the next elastic scattering angle is calculated, the new velocity
vector components v
x
, v
y
, v
z
are determined to transport the
electron to the next location. A trajectory ends when either the
electron energy falls below a threshold of interest (e.g., 1 keV),
or else the path takes it outside the geometric bounds of the
specimen, which is determined by comparing the current loca-
tion (x, y, z) with the specimen boundaries. The capability of
simulating electron beam interactions in specimens with com-
plex geometrical shapes is one of the major strengths of the
Monte Carlo electron trajectory simulation method.
Monte Carlo electron trajectory simulation can pro-
vide visual depictions as well as numerical results of the
beam–specimen interaction, creating a powerful instructional
tool for studying this complex phenomenon. Several power-
ful Monte Carlo simulations appropriate for SEM and X-ray
microanalysis applications are available as free resources:
CASINO [7 http://www.gel.usherbrooke.ca/casino/What.html]
Joy Monte Carlo [7 http://web.utk.edu/~srcutk/htm/
simulati.htm]
NIST DTSA-II [7 http://www.cstl.nist.gov/div837/837.02/
epq/dtsa2/index.html]
While the static images of Monte Carlo simulations pre-
sented below are useful instructional aids, readers are
encouraged to perform their own simulations to become
familiar with this powerful tool, which in more elaborate
implementations is an important aid in understanding criti-
cal aspects of SEM imaging.
1.4.1 What Do Individual Monte Carlo
Trajectories Look Like?
Perform a Monte Carlo simulation (CASINO simulation) for
copper with a beam energy of 20 keV and a tilt of 0° (beam
perpendicular to the surface) for a small number of trajecto-
ries, for example, 25. . Figure 1.5a, b show two simulations of
25 trajectories each. The trajectories are actually determined
in three dimensions (x-y-z, where x-y defines the surface
plane and z is perpendicular to the surface) but for plotting
are rendered in two dimensions (x-z), with the third
dimension y projected onto the x-z plane. (An example of the
true three-dimensional trajectories, simulated with the Joy
Monte Carlo, is shown in . Fig. 1.6, in which a small number
of trajectories (to minimize overlap) have been rendered as
an anaglyph stereo representation with the convention left
eye = red filter. Inspection of this simulation shows the y
motion of the electrons in and out of the x-z plane.) The sto-
chastic nature of the interaction imposed by the nature of
elastic scattering is readily apparent in the great variation
among the individual trajectories seen in . Fig. 1.5a, b. It
quickly becomes clear that individual beam electrons follow a
huge range of paths and simulating a small number of trajec-
tories does not provide an adequate view of the electron beam
specimen interaction.
1.4.2 Monte Carlo Simulation To Visualize
the Electron Interaction Volume
To capture a reasonable picture representation of the electron
interaction volume, which is the region of the specimen in
which the beam electrons travel and deposit energy, it is nec-
essary to calculate many more trajectories. . Figure 1.5c
shows the simulation for copper, E
0
= 20 keV at 0° tilt
extended to 500 trajectories, which reveals the full extent of
the electron interaction volume. Beyond a few hundred tra-
jectories, superimposing the three-dimensional trajectories
to create a two-dimensional representation reaches dimin-
ishing returns due to overlap of the plotted lines. While sim-
ulating 500 trajectories provides a reasonable qualitative
view of the electron interaction volume, Monte Carlo calcu-
lations of numerical properties of the interaction volume and
related processes, such as electron backscattering (discussed
in the backscattered electron module), are subject to statisti-
cally predictable variations because of the use of random
numbers to select the elastic scattering parameters. Variance
in repeated simulations of the same starting conditions is
related to the number of trajectories and can be described
with the properties of the Gaussian (normal) distribution.
Thus the precision, p, of the calculation of a parameter of the
interaction is related to the total number of simulated trajec-
tories, n, and the fraction, f, of those trajectories that produce
the effect of interest (e.g., backscattering):
pfnf nfn=() ()=()
−12 12//
/

(1.4)
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

7 1
Cu E
0 = 20 keV
200 nm
0.0 nm
200.0 nm
400.0 nm
600.0 nm
800.0 nm
582.5 nm-582.5 nm 291.3 nm-291.3 nm -0.0 nm
a
Cu E
0 = 20 keV
200 nm
0.0 nm
233.5 nm
466.9 nm
700.4 nm
933.8 nm
680.0 nm-680.0 nm 340.0 nm-340.0 nm -0.0 nm
c
Cu E
0 = 20 keV
200 nm
0.0 nm
180.0 nm
360.0 nm
540.0 nm
720.0 nm
524.3 nm-524.3 nm 262.1 nm-262.1 nm -0.0 nm
b
. .Fig. 1.5 a Copper, E
0
= 20 keV; 0 tilt; 25 trajec-
tories (CASINO Monte Carlo simultion). b Copper,
E
0
= 20 keV; 0 tilt; another 25 trajectories. c Copper,
E
0
= 20 keV; 0 tilt; 200 trajectories
1.4 · Simulating the Effects of Elastic Scattering: Monte Carlo Calculations

8
1
500 nm
computed BS yield = 0.31
Energy (keV)
Tilt/TOA
Number
Select
Repeat
Exit
20
35
0
. .Fig. 1.6 Three-dimensional representation of a Monte Carlo
simulation (Cu, 20 keV, 0° tilt) using the anaglyph stereo method (left
eye = red filter) (Joy Monte Carlo)
1.4.3 Using the Monte Carlo Electron
Trajectory Simulation to Study
the Interaction Volume
What Are the Main Features of the Beam
Electron Interaction Volume?
In . Fig. 1.5c, the beam electron interaction volume is seen to
be a very complex structure with dimensions extending over
hundreds to thousands of nanometers from the beam impact
point, depending on target material and the beam energy. At
0° tilt, the interaction volume is rotationally symmetric
around the beam. While the electron trajectories provide a
strong visual representation of the interaction volume, more
informative numerical information is needed. The Monte
Carlo simulation can provide detailed information on many
aspects of the electron beam–specimen interaction. The
color-encoding of the energy deposited along each trajectory,
as implemented in the Joy Monte Carlo shown in . Fig. 1.11,
creates a view that reveals the general three-dimensional
complexity of energy deposition within the interaction vol-
ume. The CASINO Monte Carlo provides an even more
detailed view of energy deposition, as shown in . Fig. 1.7.
The energy deposition per unit volume is greatest just under
the beam impact location and rapidly falls off as the periph-
ery of the interaction volume is approached. This calculation
reveals that a small cylindrical volume under the beam
impact point, shown in more detail in . Fig. 1.7b, receives
half of the total energy deposited by the beam in the speci-
men (that is, the volume within the 50% contour), with the
balance of the energy deposited in a strongly non-linear fash-
ion in the much larger portion of the interaction volume.
How Does the Interaction Volume Change
with Composition?
. Figure 1.8 shows the interaction volume in various targets,
C, Si, Cu, Ag, and Au, at fixed beam energy, E
0
= 20 keV, and
0° tilt. As the atomic number of the target increases, the lin-
ear dimensions of the interaction volume decrease. The
form also changes from pear-shaped with a dense conical
region below the beam impact for low atomic number tar-
gets to a more hemispherical shape for high atomic number
targets.
kNote the dramatic change of scale
Approximately 12 gold atoms were encountered within the
footprint of a 1-nm diameter at the surface. Without consid-
ering the effects of elastic scattering, the Bethe range for Au
at an incident beam energy of 20 keV limited the penetra-
tion of the beam to approximately 1200 nm and a cylindri-
cal volume of approximately 940 nm
3
, containing
approximately 5.6 × 10
4
Au atoms. The effect of elastic scat-
tering is to create a three-dimensional hemispherical inter-
action volume with a radius of approximately 600 nm and a
volume of 4.5 × 10
8
nm
3
, containing 2.7 × 10
10
Au atoms, an
increase of nine orders-of-magnitude over the number of
atoms encountered in the initial beam footprint on the
surface.
How Does the Interaction Volume Change
with Incident Beam Energy?
. Figure 1.9 shows the interaction volume for copper at 0° tilt
over a range of incident beam energy from 5 to 30 keV. The
shape of the interaction volume is relatively independent of
beam energy, but the size increases rapidly as the incident
beam energy increases.
How Does the Interaction Volume Change
with Specimen Tilt?
. Figure 1.10 shows the interaction volume for copper at an
incident beam energy of 20 keV and a series of tilt angles. As
the tilt angle increases so that the beam approaches the surface
at a progressively more shallow angle, the shape of the interac-
tion volume changes significantly. At 0° tilt, the interaction
volume is rotationally symmetric around the beam, but as the
tilt angle increases the interaction volume becomes asymmet-
ric, with the dense portion of the distribution shifting progres-
sively away from the beam impact point. The maximum
penetration of the beam is reduced as the tilt angle increases.
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

9 1
Cu E
0 = 20 keV
5%
10%
25%
0.0 nm
206.3 nm
412.6 nm
618.9 nm
825.2 nm
300.4 nm0.0 nm-300.4 nm
5.0%
10.0%
50.0%
90.0%
25.0%
75.0%
-600.9 nm 600.9 nm
50%
75%
90%
90%
75%
50%
25%
10%
200 nm
a
b
. .Fig. 1.7 a Isocontours of
energy loss showing fraction
remaining; Cu, 20 keV, 0° tilt;
50,000 trajectories (CASINO Monte
Carlo simulation). b Expanded
view of high density region of 1.7a
1.4 · Simulating the Effects of Elastic Scattering: Monte Carlo Calculations

10
1
E
0
= 20 keV
0° tilt
C
0.0 nm
892.6 nm
1785.3 nm
2677.9 nm
3570.6 nm
2600.0 nm
0.0 nm
755.3 nm
1510.6 nm
2265.9 nm
3021.3 nm
2200.0 nm-2200.0 nm 1100.0 nm-1100.0 nm -0.0 nm
1300.0 nm-0.0 nm-1300.0 nm-2600.0 nm
Si
Cu
Ag
Au
1 µm
. .Fig. 1.8 Monte Carlo simulations for an incident beam energy of 20 keV and 0° tilt for C, Si, Cu, Ag, and Au, all shown at the same scale
(CASINO Monte Carlo simulation)
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

11 1
Cu
0° tilt
500 nm
30 keV
20 keV
10 keV
5 keV
0.0 nm
0.0 nm
233.5 nm
466.9 nm
700.4 nm
933.8 nm
680.0 nm340.0 nm0.0 nm-340.0 nm-680.0 nm
432.6 nm
865.2 nm
1297.8 nm
1730.4 nm
1260.0 nm-1260.0 nm 630.0 nm-630.0 nm 0.0 nm
. .Fig. 1.9 Monte Carlo simula-
tions for Cu, 0° tilt, incident beam
energies 5, 10, 20, and 30 keV
(CASINO Monte Carlo simulation)
1.4 · Simulating the Effects of Elastic Scattering: Monte Carlo Calculations

12
1
1.5 A Range Equation To Estimate the Size
of the Interaction Volume
While the Monte Carlo simulation is a powerful tool to depict
the complexity of the electron beam specimen interactions, it
is often useful to have a simple estimate of the size. The Bethe
range gives the maximum distance the beam electron can
travel in the specimen, but this distance is measured along
the complex trajectory that develops because of elastic scat-
tering. Kanaya and Okayama (1972) developed a range equa-
tion that considered both inelastic and elastic scattering to
give an estimate of the interaction volume as the radius of a
hemisphere centered on the beam impact point that con-
tained at least 95% of the trajectories:
RA ZE
KO
nm
−()= ()276
089
0
167
./
..
ρ

(1.5)
where A is the atomic weight (g/mol), Z is the atomic num-
ber, ρ is the density (g/cm
3
), and E
0
is the incident beam
energy (keV). Calculations of the Kanaya–Okayama range
are presented in . Table 1.1. The Kanaya–Okayama range
0° tilt
45° tilt
60° tilt
75° tilt
Cu
500 nm
0.0 nm
233.5 nm
466.9 nm
700.4 nm
933.8 nm
0.0 nm
219.7 nm
439.5 nm
659.2 nm
878.9 nm
0.0 nm
240.0 nm
480.0 nm
720.0 nm
960.0 nm
0.0 nm
254.1 nm
508.1 nm
762.2 nm
1016.2 nm
680.0 nm340.0 nm-340.0 nm-680.0 nm 0.0 nm
640.0 nm320.0 nm-320.0 nm-640.0 nm 0.0 nm
740.0 nm370.0 nm-370.0 nm-740.0 nm 0.0 nm
699.0 nm349.5 nm-349.5 nm-699.0 nm 0.0 nm
. .Fig. 1.10 Monte Carlo simulations for Cu, 20 keV, with various tilt angles (CASINO Monte Carlo simulation)
. .Table 1.1 Kanaya–Okayama range
5 keV (nm)10 keV 20 keV 30 keV (μm)
C 450 nm 1.4 μm 4.5 μm 8.9 μm
Al 413 nm 1.3 μm 4.2 μm 8.2 μm
Fe 159 nm 505 nm 1.6 μm 3.2 μm
Ag 135 nm 431 nm 1.4 μm 2.7 μm
Au 85 nm 270 nm 860 nm 1.7 μm
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

13 1
is shown superimposed on the Monte Carlo simulation of
the interaction volume in . Fig. 1.11 and is plotted graphi-
cally in . Fig. 1.12. It is, of course, simplistic to use a single
numerical value of the range to describe such a complex phe-
nomenon as the electron interaction volume with its varying
contours of energy deposition, and thus the range equation
should only be considered as a “gray” number useful for esti-
mation purposes. Nevertheless, the Kanaya–Okayama range
is useful as a means to provide scaling to describe the spatial
distributions of the signals produced within the interaction
volume: secondary electrons, backscattered electrons, and
X-rays.
E
0
= 20 keV; 0° tilt
Carbon Aluminum
GoldCopper
1000 nm1000 nm
1000 nm
1000 nm
. .Fig. 1.11 Kanaya–Okayama range (gold arrow) superimposed on the interaction volume for C, Al, Cu, and Au at E0 = 20 keV and 0° tilt (Joy
Monte Carlo simulation)
1.5 · A Range Equation To Estimate the Size of the Interaction Volume

14
1
References
Bethe H (1930) Theory of the transmission of corpuscular radiation
through matter. Ann Phys Leipzig 5:325
CASINO 7 http://www.gel.usherbrooke.ca/casino/What.html
Joy Monte Carlo 7 http://web.utk.edu/~srcutk/htm/simulati.htm
Kanaya K, Okayama S (1972) Penetration and energy-loss theory of elec-
trons in solid targets. J Phys D Appl Phys 5:43
NIST DTSA-II 7 http://www.cstl.nist.gov/div837/837.02/epq/dtsa2/index.
html
12000
C
Al
Ag
Au
Cu
10000
8000
6000
4000
2000
0
51 02 03 02515
Incident beam energy (keV)
kanaya-okayama range
R
ange (nm)
. .Fig. 1.12 Kanaya–Okayama
range plotted for C, Al, Cu, Ag and
Au as a function of E
0
Chapter 1 ? Electron Beam?Specimen Interactions: Interaction Volume

© Springer Science+Business Media LLC 2018
J. Goldstein et al., Scanning Electron Microscopy and X-Ray Microanalysis,
https://doi.org/10.1007/978-1-4939-6676-9_2
15
Backscattered Electrons
2
2.1 Origin – 16
2.1.1 The Numerical Measure of Backscattered Electrons – 16
2.2 Critical Properties of Backscattered Electrons – 16
2.2.1 BSE Response to Specimen Composition
(η vs. Atomic Number, Z) – 16
2.2.2 BSE Response to Specimen Inclination (η vs. Surface Tilt, θ) – 20
2.2.3 Angular Distribution of Backscattering – 22
2.2.4 Spatial Distribution of Backscattering – 23
2.2.5 Energy Distribution of Backscattered Electrons – 27
2.3 Summary – 27
References – 28

16
2
2.1 Origin
Close inspection of the trajectories in the Monte Carlo simu-
lation of a flat, bulk target of copper at 0° tilt shown in
. Fig. 2.1 reveals that a significant fraction of the incident
beam electrons undergo sufficient scattering events to com-
pletely reverse their initial direction of travel into the speci-
men, causing these electrons to return to the entrance surface
and exit the specimen. These beam electrons that escape
from the specimen are referred to as “backscattered elec-
trons” (BSE) and constitute an important SEM imaging sig-
nal rich in information on specimen characteristics. The BSE
signal can convey information on the specimen composition,
topography, mass thickness, and crystallography. This mod-
ule describes the properties of backscattered electrons and
how those properties are modified by specimen characteris-
tics to produce useful information in SEM images.
2.1.1 The Numerical Measure of
Backscattered Electrons
Backscattered electrons are quantified with the “backscat-
tered electron coefficient,” η, defined as
η=NN
BSEB
/

(2.1)
where N
B
is the number of beam electrons that enter the
specimen and N
BSE
is the number of those electrons that sub-
sequently emerge as backscattered electrons.
2.2 Critical Properties of Backscattered
Electrons
2.2.1 BSE Response to Specimen
Composition (η vs. Atomic Number, Z)
Use the CASINO Monte Carlo simulation software, which
reports η in the output, to examine the dependence of electron
backscattering on the atomic number of the specimen.
Simulate at least 10,000 trajectories at an incident energy
of E
0
= 20 keV and a surface tilt of 0° (i.e., the beam is perpen-
dicular to the surface). Note that statistical variations will be
observed in the calculation of η due to the different selections
of the random numbers used in each simulation. Repetitions
of this calculation will give a distribution of results, with a
precision p = (η N)
1/2
/η N, so that for N = 10,000 trajectories
and η ~ 0.15 (Si), p is expected to be 2.5 %. . Figure 2.2 shows
the simulation of 500 trajectories in carbon, silicon, copper,
and gold with an incident energy of E
0
= 20 keV and a surface
tilt of 0°, showing qualitatively the increase in the number of
backscattered electrons with atomic number.
Detailed experimental measurements of the backscattered
electron coefficient as a function of the atomic number, Z, in
highly polished, flat pure element targets confirm a generally
monotonic increase in η with increasing Z, as shown in
. Fig. 2.3a, where the classic measurements made by Heinrich
(1966) at a beam energy of 20 keV are plotted. The slope of η
vs. Z is highest for low atomic number targets up to approxi-
mately Z =14 (Si). As Z continues to increase into the range of
500 nm
Cu
E
0 = 20 keV
0° Tilt
-582.5 nm -291.3 nm -0.0 nm 291.3 nm 582.5 nm
800.0 nm
600.0 nm
400.0 nm
200.0 nm
0.0 nm
BSE
Absorbed Electrons
(lost all energy and are
absorbed within specimen)
. .Fig. 2.1 Monte Carlo
simulation of a flat, bulk target of
copper at 0° tilt. Red trajectories
lead to backscattering events
Chapter 2 ? Backscattered Electrons

17 2
the transition elements, e.g., Z = 26 (Fe), the slope progressively
decreases until at very high Z, e.g., the region around Z = 79
(Au), the slope becomes so shallow that there is very little
change in η between adjacent elements. Plotted in addition to
the experimental measurements in . Fig. 2.3a is a mathemati-
cal fit to the 20 keV data developed by Reuter (1972):
η=+ ×+ ×−−
−−
002540016186108 310
42 73
.. ..ZZ Z

(2.2)
This fit provides a convenient estimate of η for those elements
for which direct measurements do not exist.
Experimental measurements (Heinrich 1966) have shown
that the backscattered electron coefficient of a mixture of
atoms that is homogeneous on the atomic scale, such as a
stoichiometric compound, a glass, or certain metallic alloys,
can be accurately predicted from the mass concentrations of
the elemental constituents and the values of η for those pure
elements:
ηη
mixture
=Σ
ii
C

(2.3)
where C is the mass (weight) fraction and i is an index that
denotes all of the elements involved.
When measurements of η vs. Z are made at different
beam energies, combining the experimental measurements
of Heinrich and of Bishop in . Fig. 2.3b, little dependence on
the beam energy is found from 5 to 49 keV, with all of the
measurements clustering relatively closely to the curve for
the 20 keV data shown in . Fig. 2.3a. This result is perhaps
surprising in view of the strong dependence of the dimen-
sions of the interaction volume on the incident beam energy.
The weak dependence of η upon E
0
despite the strong depen-
dence of the beam penetration upon E
0
can be understood as
a near balance between the increased energy available at
higher E
0
, the lower rate of loss, dE/ds, with higher E
0
, and
the increased penetration. Thus, although a beam electron
may penetrate more deeply at high E
0
, it started with more
C
E0 = 20 keV
1 µm
Si
E0 = 20 keV
1 µm
a b
Cu
E0 = 20 keV
500 nm
Au
E0 = 20 keV
250 nm
c
d
0.0 nm
624.9 nm
1249.7 nm
1874.6 nm
2499.4 nm
1820.0 nm910.0 nm-0.0 nm-910.0 nm-1820.0 nm
0.0 nm
755.3 nm
1510.6 nm
2265.9 nm
3021.3 nm
2200.0 nm1100.0 nm-0.0 nm-1100.0 nm-2200.0 nm
0.0 nm
233.5 nm
466.9 nm
700.4 nm
933.8 nm
680.0 nm340.0 nm-0.0 nm-340.0 nm-680.0 nm
0.0 nm
137.3 nm
274.7 nm
412.0 nm
549.3 nm
400.0 nm200.0 nm-0.0 nm-200.0 nm-400.0 nm
. .Fig. 2.2 a Monte Carlo simulation of 500 trajectories in carbon
with an incident energy of E
0
= 20 keV and a surface tilt of 0° (CASINO
Monte Carlo simulation). b Monte Carlo simulation of 500 trajectories
in silicon with an incident energy of E
0
= 20 keV and a surface tilt of 0°.
c Monte Carlo simulation of 500 trajectories in copper with an incident
energy of E
0
= 20 keV and a surface tilt of 0°. d Monte Carlo simulation
of 500 trajectories in gold with an incident energy of E
0
= 20 keV and a
surface tilt of 0°. Red trajectories = backscattering
2.2 · Critical Properties of Backscattered Electrons

18
2
energy and lost that energy at a lower initial rate than an elec-
tron at a lower incidence energy. Thus, a higher incidence
energy electron, despite penetrating deeper in the specimen,
retains more energy and can continue to scatter and progress
through the target to escape.
SEM Image Contrast with BSE: “Atomic
Number Contrast”
Whenever a signal that can be measured in the SEM, such as
backscattered electrons, follows a predictable response to a
specimen property of interest, such as composition, the phys-
ical basis for a “contrast mechanism” is established. Contrast,
C
tr
, is defined as
Electron backscatter vs. atomic number (E
0 = 20 keV)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
02 04 0
Atomic number
Backscatter coefficien
t
60 80
Reuter Fit
Heinrich 20 keV data
100
0.6
0.5
0.4
0.3
0.2
0.1
0.0
02 04 0
Atomic number
Heinrich 10 keV
Heinrich 20 keV
Heinrich 30 keV
Heinrich 40 keV
Heinrich 49 keV
Bishop 5 keV
Reuter fit 20 keV
Electron backscattering vs. atomic number
Backscatter coefficien
t
60 80 100
a
b
. .Fig. 2.3 a Electron backscatter
coefficient as a function of atomic
number for pure elements (Data of
Heinrich 1966; fit of Reuter 1972).
b Electron backscatter coefficient
as a function of atomic number for
pure elements for incident beam
energies of 5 keV (data of Bishop
1966); 10 keV to 49 keV (Data of
Heinrich 1966); Reuter’s fit to Hein-
rich’s 20 keV data, (1972))
Chapter 2 ? Backscattered Electrons

19 2
CS SS SS
tr
with=() >
21 22 1
−/

(2.4)
where S is the signal measured at any two locations of interest
in the image field. As shown in . Fig. 2.4, examples include
the contrast between an object P
1
and the general back-
ground P
2
or between two objects that share an interface, P
3

and P
4
. By this definition, contrast can range numerically
from 0 to 1.
The monotonic behavior of η vs. Z establishes the physical
basis for “atomic number contrast” (also known as
“Z-contrast” and “compositional contrast”). When an SEM
BSE image is acquired from a flat specimen (i.e., no topogra-
phy is present, at least on a scale no greater than about 5 % of
the Kanaya–Okayama range for the particular material com-
position and incident beam energy), then local differences in
composition can be observed as differences in the BSE inten-
sity, which can be used to construct a meaningful gray-scale
SEM image. The compositionally-different objects must have
dimensions that are at least as large as the Kanaya-Okayama
range for each distinct material so that a BSE signal charac-
teristic of the particular composition can be measured over at
least the center portion of the object. The BSE signal at beam
locations on the edge of the object may be affected by pene-
tration into the neighboring material(s).
From the definition of contrast, C
tr
, atomic number con-
trast can be predicted between two materials with backscat-
ter coefficients η
1
and η
2
when the measured signal S is
proportional to η:
C
tr
with=() >ηη ηη η
21 22 1
−/

(2.5)
An example of atomic number contrast from a polished cross
section of an aluminum-nickel alloy (Raney nickel) is shown
in . Fig. 2.5. At least four distinct gray levels are observed,
which correspond to three different Al/Ni phases with differ-
ent Al-Ni compositions (labeled “1,” “3,” and “4” in . Fig. 2.5)
and a fourth phase that consists of Al-Fe-Ni (labelled “2”),
with the phase containing the highest nickel concentration
appearing brightest in the BSE image.
•P
2
•P
1
P
3
P
4
. .Fig. 2.4 Illustration of some possible contrast situations of inter-
est, e.g., an object P1 and the general background P2 or between two
objects that share an interface, P3 and P4
4
3
21
10 µm
. .Fig. 2.5 Backscattered electron atomic
number contrast for a polished flat surface of
Raney nickel (nickel-aluminum) alloy. Numbered
locations identify phases with distinctly different
compositions
2.2 · Critical Properties of Backscattered Electrons

20
2
2.2.2 BSE Response to Specimen Inclination
(η vs. Surface Tilt, θ)
Model the effect of the angle of inclination of the specimen sur-
face to the incident beam with the Monte Carlo simulation.
Select a particular element and incident beam energy, e.g., cop-
per and E
0
= 20 keV, and vary the angle of incidence. Calculate
at least 10,000 trajectories to obtain adequate simulation
precision.
. Figure 2.6 shows simulations for aluminum with an
incident beam energy of 15 keV at various inclinations calcu-
lated with 200 trajectories, which qualitatively reveals the
increase in backscattering in a forward direction (i.e., con-
tinuing in the general direction of the incident beam) with
increasing tilt angle. A more extensive series of simulations
for aluminum at E
0
= 15 keV with 25,000 trajectories cover-
ing a greater range of specimen tilts is presented in . Table 2.1,
where the backscatter coefficient shows a strong dependence
on the surface inclination.
Al
0∞ tilt
500 nm
E
0
= 15 keV
Al
500 nm
E
0
= 15 keV
45∞ tilt
AI
-1420.2 nm
AI
-710.0 nm -0.0 nm 710.0 nm 1420.0 nm
1950.1 nm
1462.6 nm
975.0 nm
487.5 nm
0.0 nm
-961.2 nm-480.6 nm -0.0 nm 480.6 nm 961.2 nm
1320.0 nm
990.0 nm
660.0 nm
330.0 nm
0.0 nm
a b
Al
500 nm
E
0
= 15 keV
60∞ tilt
Al
500 nm
E
0
= 15 keV
75∞ tilt
AI
-1223.3 nm-611.7 nm -0.0 nm 611.7 nm 1223.3 nm
1680.0 nm
1260.0 nm
840.0 nm
420.0 nm
0.0 nmAI
-699.0 nm -349.5 nm -0.0 nm 349.5 nm 699.0 nm
960.0 nm
720.0 nm
480.0 nm
240.0 nm
0.0 nm
c d
. .Fig. 2.6 a Monte Carlo simulation for aluminum at E
0
= 15 keV for
a tilt angle of 0°. b Monte Carlo simulation for aluminum at E
0
= 15 keV
for a tilt angle of 45°. c Monte Carlo simulation for aluminum at
E
0
= 15 keV for a tilt angle of 60°. d Monte Carlo simulation for alumi-
num at E
0
= 15 keV for a tilt angle of 75°
. .Table 2.1 Backscatter vs. tilt angle for aluminum at
E
0
= 15 keV (25,000 trajectories calculated with the CASINO
Monte Carlo simulation)
Tilt (degrees) η
0 0.129
15 0.138
30 0.169
45 0.242
60 0.367
75 0.531
80 0.612
85 0.706
88 0.796
89 0.826
Chapter 2 ? Backscattered Electrons

21 2
. Figure 2.7 shows the results of similar Monte Carlo
simulations for various elements as a function of surface
inclination. As the surface tilt increases, η increases for all
elements, converging toward unity at high tilt and grazing
incidence for the incident beam.
SEM Image Contrast: “BSE Topographic
Contrast—Number Effects”
This regular behavior of η vs. θ provides the basis for a
contrast mechanism by which differences in the relative
numbers of backscattered electrons depend on differences
in the local surface inclination, which reveals the surface
topography. . Figure 2.8a shows an example of a pure
material (polycrystalline silver) with grain faces inclined
at various angles. The higher the inclination of the local
surface to the incident beam, the higher will be the BSE
signal, so that highly inclined surfaces appear bright, while
dark surfaces are those nearly perpendicular to the beam.
This image was prepared with a backscattered electron
detector (discussed in the Electron Optics—Detectors
module), which has a very large solid angle, so that back-
scattered electrons are collected with high efficiency
regardless of the direction that they travel after leaving the
specimen.
Electron backscattering vs tilt angle
1.0
0.8
0.6
0.4
0.2
0.0
02 04 0
Tilt angle (degrees)
Backscatter coefficien
t
8060
C
Al
Cu
Ag
Au
. .Fig. 2.7 Monte Carlo calcula-
tions of electron backscattering
from various tilted pure element
bulk targets
5 µm5 µm
a b
. .Fig. 2.8 a SEM backscattered electron image of a topographically
irregular surface of pure silver prepared with a large collection angle
BSE detector. b SEM backscattered electron image of the same area,
prepared with a small collection angle BSE detector placed at the top
of the image looking down
2.2 · Critical Properties of Backscattered Electrons

22
2
2.2.3 Angular Distribution of Backscattering
Beam Incident Perpendicular to the Specimen
Surface (0° Tilt)
For a flat, bulk target, backscattered electrons emerge
through the surface along a wide range of possible angular
paths measured relative to the surface normal. When the
incident beam is perpendicular to the specimen surface (0°
tilt), experimental measurements and Monte Carlo simula-
tions show that the angular distribution of the trajectories is
such that the fraction along any given angle of emission is
proportional to the cosine of that angle of emission, φ,
between the electron trajectory and the surface normal, as
shown in . Fig. 2.9a:
ηϕ ϕ() ()~cos

(2.6)
Thus, the largest number of BSEs follow a path parallel to the
surface normal (φ =0°, cosine = 1), while virtually no BSEs
exit along a trajectory nearly parallel to the surface (φ =90°,
cosine = 0). The angular distribution seen in . Fig. 2.8a is also
rotationally symmetric around the beam: the same cosine
shape would be found in any section through the distribution
in any plane perpendicular to surface containing the beam
vector and surface normal.
Beam Incident at an Acute Angle
to the Specimen Surface (Specimen
Tilt > 0°)
When a flat, bulk target is tilted so that the beam is incident at
an acute angle to the surface, the angular distribution of back-
scattered electrons changes from the rotationally symmetric
cosine function of . Fig. 2.9a to the asymmetric distribution
Incident beam
Surface normal
330 30
60
90
300
a
270
BSE
Flat specimen
1.0
0.8
0.6
0.4
0.2
0.0
0.00.21.00.80.60.4 0.40.60.81.00.2
ϕ
0
180
150
BSE
Surface
normal
dh/dW
Beam
120
60 degrees specimen tilt = beam incidence 30 degrees above surface
90
60
30
0.20
0.25
0.15
0.05
0.00 0
0.250.200.150.100.050.000.050.100.150.200.25
0.10
b
. .Fig. 2.9 a Cosine angular distribution
observed for the directionality of backscatter-
ing from a bulk target at normal incidence (0º
tilt; beam perpendicular to surface). b Angu-
lar distribution observed for the directionality
of backscattering from a bulk target inclined
(60° tilt; beam 30° above surface) (Data of
Seidel quoted by Niedrig 1978)
Chapter 2 ? Backscattered Electrons

23 2
seen in . Fig. 2.9b, with this distribution measured for a tilt of
60° (angle of incidence = 30°). The angular distribution is
peaked in the forward direction away from the incident beam
direction, with the maximum BSE emission occurring at an
angle above the surface close to the value of the angle of inci-
dence above the surface of the beam. This angular asymmetry
develops slowly for tilt angles up to approximately 30°, but the
asymmetry becomes increasingly pronounced with further
increases in the specimen tilt. Moreover, the rotational sym-
metry of the 0° tilt case is also progressively lost with increas-
ing tilt, with the asymmetric distribution seen in . Fig. 2.9b
becoming much narrower in the direction out of the plotting
plane. See 7 Chapter 29 for effects of crystal structure on
backscattering angular distribution.
SEM Image Contrast: “BSE Topographic
Contrast—Trajectory Effects”
The overall effects of specimen tilt are to increase the number
of backscattered electrons and to create directionality in the
backscattered electron emission, and both effects become
increasingly stronger as the tilt increases. The “trajectory
effects” create a very strong component of topographic con-
trast when viewed with a backscattered electron detector that
has limited size and is placed preferentially on one side of the
specimen. . Figure 2.8b shows the same area as . Fig. 2.8a
imaged with a small solid angle detector, located at the top
center of the image. Very strong contrast is created between
faces tilted toward the detector, i.e., facing upward, and those
tilted away, i.e., facing downward. These effects will be dis-
cussed in detail in the Image Interpretation module.
2.2.4 Spatial Distribution of Backscattering
Model a small number of trajectories (~25) so that the indi-
vidual trajectories can be distinguished; e.g., for a copper target
with an incident beam energy of 20 keV and 0° tilt, as seen in
. Fig. 2.10 (Note: because of the random number sampling,
repeated simulations will differ from each other and will be dif-
ferent from the printed example.) By following a number of
trajectories from the point of incidence to the point of escape
through the surface as backscattered electrons, it can be seen
that the trajectories of beam electrons that eventually emerge
as BSEs typically traverse the specimen both laterally and in
depth.
Depth Distribution of Backscattering
By performing detailed Monte Carlo simulations for many
thousands of trajectories and recording for each trajectory
the maximum depth of penetration into the specimen before
the electron eventually escaped as a BSE, we can determine
the contribution to the overall backscatter coefficient as a
function of the depth of penetration, as shown for a series of
elements in . Fig. 2.11a. To compare the different elements,
the horizontal axis of the plot is the depth normalized by the
Kanaya–Okayama range for each element. From the depth
distribution data in . Fig. 2.11a, the cumulative backscatter-
ing coefficient as a function of depth can be calculated, and as
shown in . Fig. 2.11b, this distribution follows an S-shaped
curve. To capture 90 % of the total backscattering, which cor-
responds to the region where the slope of the plot is rapidly
decreasing, the backscattered electrons are found to travel a
Cu
E
0
= 20 keV
0
º
tilt
500 nm
-640.0 nm -320.0 nm -0.0 nm 320.0 nm 640.0 nm
878.9 nm
659.2 nm
439.5 nm
219.7 nm
0.0 nmMaximum
depth of
penetration
for this
trajectory
leading to BSE.
Cu
. .Fig. 2.10 Monte Carlo simu-
lation of a few trajectories in
copper with an incident beam
energy of 20 keV and 0° tilt to
show effect of penetration depth
of backscattered electrons
2.2 · Critical Properties of Backscattered Electrons

24
2
significant fraction of the Kanaya–Okayama range into the
target. Strong elastic scattering materials with high atomic
number such as gold sample a smaller fraction of the range
than the weak elastic scattering materials such as carbon.
. Table 2.2 lists the fractional range to capture 90 % of back-
scattering at normal beam incidence (0° tilt) and for a similar
Monte Carlo study performed for a target at 45° tilt. For a
tilted target, all materials show a slightly smaller fraction of
the Kanaya–Okayama range to reach 90 % backscattering
compared to the normal incidence case.
When the beam energy is increased for a specific mate-
rial, the strong dependence of the total range on the incident
Backscattering vs. depth
1.0
0.8
0.6
C
AI
Cu
Ag
Au
0.4
0.2
0.0
0.0 0.1
0.155
0.185
0.205
0.250
0.285
0.2
Depth/range (Kanaya-Okayama)
C
umulative backscattering (normalized)
0.3 0.4
Backscattered electron penetration
0.08
0.06
0.04
0.02
Backscatter frac
tion
0.00
0.0 0.1 0.2
Depth/range (Kanaya-Okayama)
0.3 0.4 0.5
C
AI
Cu
Ag
Aua
b
. .Fig. 2.11 a Distribution
of depth penetration of back-
scattered electrons in various
elements. b Cumulative backscat-
tering coefficient as a function
of the depth of penetration in
various elements, showing deter-
mination of 90 % total backscat-
tering depth
Chapter 2 ? Backscattered Electrons

25 2
beam energy leads to a strong dependence of the sampling
depth of backscattered electrons, as shown in the depth dis-
tributions of backscattered electrons for copper over a wide
energy range in . Fig. 2.12. The substantial sampling depth
of backscattered electrons combined with the strong depen-
dence of the electron range on beam energy provides a useful
tool for the microscopist. By comparing a series of images of
a given area as a function of beam energy, subsurface details
can be recognized. An example is shown in . Fig. 2.13 for an
engineered semiconductor electronic device with three-
dimensional layered features, where a systematic increase in
the beam energy reveals progressively deeper structures.
Radial Distribution of Backscattered
Electrons
The Monte Carlo simulation can record the x-y location at
which a backscattered electron exits through the surface
plane, and this information can be used to calculate the
radial distribution of backscattering relative to the beam
impact location. The cumulative radial distribution is shown
in . Fig. 2.14 for a series of elements, as normalized by the
Kanaya–Okayama range for each element, and an S-shaped
curve is observed. . Table 2.3 gives the fraction of the range
necessary to capture 90 % of the total backscattering. The
radial distribution is steepest for high atomic number ele-
ments, which scatter strongly compared to weakly scattering
low atomic number elements. However, even for strongly
scattering elements, the backscattered electrons emerge over
a significant fraction of the range. This characteristic impacts
the spatial resolution that can be obtained with backscat-
tered electron images. An example is shown in . Fig. 2.15 for
an interface between an aluminum-rich phase and a copper-
rich phase (CuAl
2
) in directionally solidified aluminum-
copper eutectic alloy. The interfaces are perpendicular to the
surface and are atomically sharp. The backscattered electron
signal response as the beam is scanned across the interface is
more than an order-of-magnitude broader (~300 nm) due to
the lateral spreading of backscattering than would be pre-
dicted from the incident beam diameter alone (10 nm).
. .Fig. 2.12 Backscattered elec-
tron depth distributions at vari-
ous energies in copper at 0° tilt
. .Table 2.2 BSE penetration depth (D/R
K-O
) to capture 90 % of
total backscattering
0º tilt 45º tilt
C 0.285 0.23
Al 0.250 0.21
Cu 0.205 0.19
Ag 0.185 0.17
Au 0.155 0.15
2.2 · Critical Properties of Backscattered Electrons

26
2
5 keV 10 keV
20 keV 30 keV
. .Fig. 2.13 BSE images at various incident beam energies of a semiconductor device consisting of silicon and various metallization layers at dif-
ferent depths
. .Fig. 2.14 Cumulative radial distribution
of backscattered electrons in various bulk
pure elements at 0° tilt showing determina-
tion of 90 % total backscattering radius
Chapter 2 ? Backscattered Electrons

27 2
2.2.5 Energy Distribution of Backscattered
Electrons
As a beam electron travels in the specimen, inelastic scatter-
ing progressively diminishes the energy. When the trajectory
of a beam electron intersects a specimen surface so that back-
scattering occurs, the backscattered electron will have lost a
portion of the initial beam energy, E
0
, with the amount lost
depending on the length of the path within the specimen.
The Monte Carlo simulation can record the exit energy of
each backscattered electron, and from this data the energy
distribution of BSE can be calculated, as shown in . Fig. 2.16a.
The energy distribution is seen to extend from the incident
beam energy down to zero energy. The energy distribution is
sharply peaked at high fractional energy for a strong elastic
scattering material such as gold, but the energy distribution
is much broader and flatter for a weak elastic scattering mate-
rial such as carbon. The backscattered electron energy spec-
tra of . Fig. 2.16a can be used to calculate the cumulative
backscattering distribution as a function of the fractional
energy retained, E/E
0
, as shown in . Fig. 2.16b. It is worth
noting that even for weakly scattering carbon, more than half
of the backscattered electrons retain at least half of the inci-
dent beam energy. The retained energy is a critical property
that impacts the design of detectors for backscattered
electrons.
2.3 Summary
Backscattered electrons form an important imaging signal
for the SEM. A general understanding of the major proper-
ties of BSE provides the basis for interpreting images:
1. η vs. Z (atomic number)
2. η vs. θ (specimen tilt)
3. η(θ) vs. φ (emission angle relative to surface normal)
4. η vs. sampling depth
5. η vs. radial distance from beam
6. η(E) vs. Z, energy distribution of BSE (. Fig. 2.16)
. .Table 2.3 Fraction of the BSE radial distribution (r/R
K-O
) to
capture 90 % of backscattering
C 0.60
Al 0.53
Cu 0.45
Ag 0.40
Au 0.34
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vector indicated in . Fig. 2.15a showing BSE signal profile
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Footnotes
Ch. E. Gover, “The Pongol Festival in Southern India,”
Journal of the Royal Asiatic Society, N.S., v. (1870) pp. 96
sq.
W. Crooke, Popular Religion and Folk-lore of Northern India
(Westminster, 1896), ii. 314 sqq.; Captain G. R. Hearn,
“Passing through the Fire at Phalon,” Man, v. (1905) pp.
154 sq. On the custom of walking through fire, or rather
over a furnace, see Andrew Lang, Modern Mythology
(London, 1897), pp. 148-175; id., in Athenaeum, 26th
August and 14th October, 1899; id., in Folk-lore, xii. (1901)
pp. 452-455; id., in Folk-lore, xiv. (1903) pp. 87-89. Mr.
Lang was the first to call attention to the wide prevalence
of the rite in many parts of the world.
Pandit Janardan Joshi, in North Indian Notes and Queries,
iii. pp. 92 sq., § 199 (September, 1893); W. Crooke, Popular
Religion and Folk-lore of Northern India (Westminster,
1896), ii. 318 sq.
E. T. Atkinson, “Notes on the History of Religion in the
Himalayas of the N.W. Provinces,” Journal of the Asiatic
Society of Bengal, liii. Part i. (Calcutta, 1884) p. 60.
Compare W. Crooke, Popular Religion and Folk-lore of
Northern India (Westminster, 1896), ii. 313 sq.
See above, vol. i. pp. 136 sq.

7.
8.
9.
10.
G. Schlegel, Uranographie Chinoise (The Hague and
Leyden, 1875), pp. 143 sq.; id., “La fête de fouler le feu
célébrée en Chine et par les Chinois à Java,” Internationales
Archiv für Ethnographie, ix. (1896) pp. 193-195. Compare
J. J. M. de Groot, The Religious System of China, vi.
(Leyden, 1910) pp. 1292 sq. According to Professor
Schlegel, the connexion between this festival and the old
custom of solemnly extinguishing and relighting the fire in
spring is unquestionable.
The Dying God, p. 262.
(Sir) H. H. Risley, Tribes and Castes of Bengal, Ethnographic
Glossary (Calcutta, 1891-1892), i. 255 sq. Compare W.
Crooke, Popular Religion and Folk-lore of Northern India
(Westminster, 1896), i. 19; id., Tribes and Castes of the
North-Western Provinces and Oudh (Calcutta, 1896), ii.
355. According to Sir Herbert Risley, the trench filled with
smouldering ashes is so narrow (only a span and a quarter
wide) “that very little dexterity would enable a man to walk
with his feet on either edge, so as not to touch the
smouldering ashes at the bottom.”
W. Crooke, Tribes and Castes of the North-Western
Provinces and Oudh, ii. 82.
M. J. Walhouse, “Passing through the Fire,” Indian
Antiquary, vii. (1878) pp. 126 sq. Compare J. A. Dubois,
Mœurs, Institutions et Cérémonies des Peuples de l'Inde
(Paris, 1825), ii. 373; E. Thurston, Ethnographic Notes in
Southern India (Madras, 1906), pp. 471-486; G. F. D'Penha,
in Indian Antiquary, xxxi. (1902) p. 392; “Fire-walking in
Ganjam,” Madras Government Museum Bulletin, vol. iv. No.
3 (Madras, 1903), pp. 214-216. At Akka timanhully, one of
the many villages which help to make up the town of
Bangalore in Southern India, one woman at least from
every house is expected to walk through the fire at the
village festival. Captain J. S. F. Mackenzie witnessed the

11.
12.
13.
14.
ceremony in 1873. A trench, four feet long by two feet
wide, was filled with live embers. The priest walked through
it thrice, and the women afterwards passed through it in
batches. Capt. Mackenzie remarks: “From the description
one reads of walking through fire, I expected something
sensational. Nothing could be more tame than the
ceremony we saw performed; in which there never was nor
ever could be the slightest danger to life. Some young girl,
whose soles were tender, might next morning find that she
had a blister, but this would be the extent of harm she
could receive.” See Captain J. S. F. Mackenzie, “The Village
Feast,” Indian Antiquary, iii. (1874) pp. 6-9. But to fall on
the hot embers might result in injuries which would prove
fatal, and such an accident is known to have occurred at a
village in Bengal. See H. J. Stokes, “Walking through Fire,”
Indian Antiquary, ii. (1873) pp. 190 sq. At Afkanbour, five
days' march from Delhi, the Arab traveller Ibn Batutah saw
a troop of fakirs dancing and even rolling on the glowing
embers of a wood fire. See Voyages d'Ibn Batoutah (Paris,
1853-1858), ii. 6 sq., iii. 439.
Sonnerat, Voyage aux Indes orientales et à la Chine (Paris,
1782), i. 247 sq.
Madras Government Museum, Bulletin, vol. iv. No. 1
(Madras, 1901), pp. 55-59; E. Thurston, Ethnographic
Notes in Southern India (Madras, 1906), pp. 471-474. One
of the places where the fire-festival in honour of Draupadi
takes place annually is the Allandur Temple, at St. Thomas's
Mount, near Madras. Compare “Fire-walking Ceremony at
the Dharmaraja Festival,” The Quarterly Journal of the
Mythic Society, vol. ii. No. 1 (October, 1910), pp. 29-32.
E. Thurston, Castes and Tribes of Southern India (Madras,
1909), i. 98 sq.; id., Ethnographic Notes in Southern India
(Madras, 1906), pp. 476 sq.

15.
16.
17.
E. Thurston, Castes and Tribes of Southern India (Madras,
1909), i. 100 sq.
F. Metz, The Tribes inhabiting the Neilgherry Hills, Second
Edition (Mangalore, 1864), p. 55.
“A Japanese Fire-walk,” American Anthropologist, New
Series, v. (1903) pp. 377-380. The ceremony has been
described to me by two eye-witnesses, Mr. Ernest Foxwell
of St. John's College, Cambridge, and Miss E. P. Hughes,
formerly Principal of the Teachers' Training College,
Cambridge. Mr. Foxwell examined the feet of the
performers both before and after their passage through the
fire and found no hurt. The heat was so great that the
sweat ran down him as he stood near the bed of glowing
charcoal. He cannot explain the immunity of the
performers. He informs me that the American writer
Percival Lowell walked in the fire and was burned so
severely that he was laid up in bed for three weeks; while
on the other hand a Scotch engineer named Hillhouse
passed over the hot charcoal unscathed. Several of Miss
Hughes's Japanese pupils also went through the ordeal with
impunity, but one of them burned a toe. Both before and
after walking through the fire the people dipped their feet
in a white stuff which Miss Hughes was told was salt.
Compare W. G. Aston, Shinto (London, 1905), p. 348: “At
the present day plunging the hand into boiling water,
walking barefoot over a bed of live coals, and climbing a
ladder formed of sword-blades set edge upwards are
practised, not by way of ordeal, but to excite the awe and
stimulate the piety of the ignorant spectators.”
Basil Thomson, South Sea Yarns (Edinburgh and London,
1894), pp. 195-207. Compare F. Arthur Jackson, “A Fijian
Legend of the Origin of the Vilavilairevo or Fire Ceremony,”
Journal of the Polynesian Society, vol. iii. No. 2 (June,
1894), pp. 72-75; R. Fulton, “An Account of the Fiji Fire-

18.
19.
20.
21.
22.
23.
24.
walking Ceremony, or Vilavilairevo, with a probable
explanation of the mystery,” Transactions and Proceedings
of the New Zealand Institute, xxxv. (1902) pp. 187-201;
Lieutenant Vernon H. Haggard, in Folk-lore, xiv. (1903) pp.
88 sq.
S. P. Langley, “The Fire-walk Ceremony in Tahiti,” Report of
the Smithsonian Institution for 1901 (Washington, 1902),
pp. 539-544; id., in Folk-lore, xiv. (1901) pp. 446-452;
“More about Fire-walking,” Journal of the Polynesian
Society, vol. x. No. 1 (March, 1901), pp. 53 sq. In his
Modern Mythology (pp. 162-165) Andrew Lang quotes from
The Polynesian Society's Journal, vol. ii. No. 2, pp. 105-108,
an account of the fire-walk by Miss Tenira Henry, which
seems to refer to Raiatea, one of the Tahitian group of
islands.
Annales de l'Association de la Propagation de la Foi, lxix.
(1897) pp. 130-133. But in the ceremony here described
the chief performer was a native of Huahine, one of the
Tahitian group of islands. The wood burned in the furnace
was hibiscus and native chestnut (Inocarpus edulis). Before
stepping on the hot stones the principal performer beat the
edge of the furnace twice or thrice with ti leaves
(dracaena).
Les Missions Catholiques, x. (1878) pp. 141 sq.; A. Lang,
Modern Mythology, p. 167, quoting Mr. Henry R. St. Clair.
Peter Kolben, The Present State of the Cape of Good Hope,
Second Edition (London, 1738), i. 129-133.
A. C. Hollis, The Nandi (Oxford, 1909), pp. 45 sq.
Rev. Joseph Shooter, The Kafirs of Natal (London, 1857), p.
35.
Diego de Landa, Relation des choses de Yucatan (Paris,
1864), pp. 231, 233.

25.
26.
27.
28.
Strabo, xii. 2. 7, p. 537. Compare Adonis, Attis, Osiris,
Second Edition, pp. 89, 134 sqq.
Pliny, Nat. Hist. vii. 19; Virgil, Aen. xi. 784 sqq. with the
comment of Servius; Strabo, v. 2. 9, p. 226; Dionysius
Halicarnasensis, Antiquit. Rom. iii. 32. From a reference to
the custom in Silius Italicus (v. 175 sqq.) it seems that the
men passed thrice through the furnace holding the entrails
of the sacrificial victims in their hands. The learned but
sceptical Varro attributed their immunity in the fire to a
drug with which they took care to anoint the soles of their
feet before they planted them in the furnace. See Varro,
cited by Servius, on Virgil, Aen. xi. 787. The whole subject
has been treated by W. Mannhardt (Antike Wald- und
Feldkulte, Berlin, 1877, pp. 327 sqq.), who compares the
rites of these “Soranian Wolves” with the ceremonies
performed by the brotherhood of the Green Wolf at
Jumièges in Normandy. See above, vol. i. pp. 185 sq.
L. Preller (Römische Mythologie,
3
i. 268), following G.
Curtius, would connect the first syllable of Soranus and
Soracte with the Latin sol, “sun.” However, this etymology
appears to be at the best very doubtful. My friend Prof. J.
H. Moulton doubts whether Soranus can be connected with
sol; he tells me that the interchange of l and r is rare. He
would rather connect Soracte with the Greek ὕραξ, “a
shrew-mouse.” In that case Apollo Soranus might be the
equivalent of the Greek Apollo Smintheus, “the Mouse
Apollo.” Professor R. S. Conway also writes to me (11th
November 1902) that Soranus and Soracte “have nothing to
do with sol; r and l are not confused in Italic.”
Livy, xxvi. 11. About this time the Carthaginian army
encamped only three miles from Rome, and Hannibal in
person, at the head of two thousand cavalry, rode close up
to the walls and leisurely reconnoitered them. See Livy,
xxvi. 10; Polybius, ix. 5-7.

29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
Above, p. 1.
Above, p. 15.
Above, pp. 13 sq.
Above, p. 8, compare p. 3.
J. J. M. de Groot, The Religious System of China, i. (Leyden,
1892), p. 355; id. vi. (Leyden, 1910) p. 942.
Rev. J. H. Gray, China (London, 1878), i. 287, 305; J. J. M.
de Groot, op. cit. i. 32, vi. 942.
J. J. M. de Groot, op. cit. i. 137, vi. 942.
J. G. Gmelin, Reise durch Sibirien (Göttingen, 1751-1752), i.
333.
W. L. Priklonski, “Ueber das Schamenthum bei den
Jakuten,” in A. Bastian's Allerlei aus Volks- und
Menschenkunde (Berlin, 1888), i. 219. Compare Vasilij
Priklonski, “Todtengebräuche der Jakuten,” Globus, lix.
(1891) p. 85.
J. A. H. Louis, The Gates of Thibet (Calcutta, 1894), p. 116.
E. Allegret, “Les Idées religieuses des Fañ (Afrique
Occidentale),” Revue de l'Histoire des Religions, l. (1904) p.
220.
A. B. Ellis, The Ewe-speaking Peoples of the Slave Coast of
West Africa (London, 1890), p. 160.
Above, pp. 162, 163, 211, 212, 214, 215, 217.
See the references above, vol. i. p. 342 note 2.
See the references above, vol. i. p. 342 note 3.
See The Magic Art and the Evolution of Kings, ii. 52 sqq.,
127; The Scapegoat, pp. 157 sqq. Compare R. Kühnau,
Schlesische Sagen (Berlin, 1910-1913), iii. p. 69, No. 1428:
“In the county of Glatz the people believe that on Walpurgis

45.
46.
47.
48.
49.
50.
51.
52.
Night (the Eve of May Day) the witches under cover of the
darkness seek to harm men in all sorts of ways. To guard
themselves against them the people set small birch trees in
front of the house-door on the previous day, and are of
opinion that the witches must count all the leaves on these
little trees before they can get into the house. While they
are still at this laborious task, the day dawns and the
dreaded guests must retire to their own realm”; id., iii. p.
39, No. 1394: “On St. John's Night (between the 23rd and
24th of June) the witches again busily bestir themselves to
force their way into the houses of men and the stalls of
cattle. People stick small twigs of oak in the windows and
doors of the houses and cattle-stalls to keep out the
witches. This is done in the neighbourhood of Patschkau
and generally in the districts of Frankenstein, Münsterberg,
Grottkau, and Neisse. In the same regions they hang
garlands, composed of oak leaves intertwined with flowers,
at the windows. The garland must be woven in the house
itself and may not be carried over any threshold; it must be
hung out of the window on a nail, which is inserted there.”
Similar evidence might be multiplied almost indefinitely.
The Golden Bough, Second Edition (London, 1900), ii. 314-
316.
The Dying God, pp. 249 sqq.
Above, vol. i. p. 117, compare pp. 143, 144.
See above, vol. i. p. 120.
The Magic Art and the Evolution of Kings, ii. 56 sqq.
Above, vol. i. pp. 120, 167.
Above, vol. i. pp. 115 sq., 116, 142, 173 sq., 185, 191, 192,
193, 209.
Above, vol. i. p. 120.

53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
Above, vol. i. p. 116. But the effigy is called the Witch.
The chapter has since been expanded into the four volumes
of The Dying God, Spirits of the Corn and of the Wild, and
The Scapegoat.
The Dying God, p. 262.
Above, pp. 9, 10, 14.
Among the Klings of Southern India the ceremony of
walking over a bed of red-hot ashes is performed by a few
chosen individuals, who are prepared for the rite by a devil-
doctor or medicine-man. The eye-witness who describes
the ceremony adds: “As I understood it, they took on
themselves and expiated the sins of the Kling community
for the past year.” See the letter of Stephen Ponder, quoted
by Andrew Lang, Modern Mythology (London, 1897), p.
160.
The Dying God, pp. 205 sqq.; Spirits of the Corn and of the
Wild, i. 216 sqq.
Above, vol. i. p. 120.
Above, vol. i. p. 186.
Above, vol. i. p. 148.
Above, vol. i. p. 233.
Above, vol. i. p. 194.
W. Mannhardt, Baumkultus, p. 524.
Bavaria, Landes- und Volkskunde des Königreichs Bayern
(Munich, 1860-1867), iii. 956; W. Mannhardt, Baumkultus,
p. 524. In the neighbourhood of Breitenbrunn the lad who
collects fuel at this season has his face blackened and is
called “the Charcoal Man” (Bavaria, etc., ii. 261).
A. Birlinger, Volksthümliches aus Schwaben (Freiburg im
Breisgau, 1861-1862), ii. 121 sq., § 146; W. Mannhardt,

67.
68.
69.
70.
71.
72.
73.
Baumkultus, pp. 524 sq.
E. Meier, Deutsche Sagen, Sitten und Gebräuche aus
Schwaben (Stuttgart, 1852), pp. 428 sq., §§ 120, 122; O.
Freiherr von Reinsberg-Düringsfeld, Das festliche Jahr
(Leipsic, 1863), p. 194; J. A. E. Köhler, Volksbrauch,
Aberglauben, Sagen und andre alte Ueberlieferungen im
Voigtlande (Leipsic, 1867), p. 176; J. V. Grohmann,
Aberglauben und Gebräuche aus Böhmen und Mähren
(Prague and Leipsic, 1864), p. 49, § 311; W. J. A. Tettau
und J. D. H. Temme, Die Volkssagen Ost-preussens,
Litthauens und West-preussens (Berlin, 1837), pp. 277 sq.;
K. Haupt, Sagenbuch der Lausitz (Leipsic, 1862-1863), i.
48; R. Eisel, Sagenbuch des Voigtlandes (Gera, 1871), p.
31, Nr. 62.
Montanus, Die deutschen Volksfeste, Volksbräuche und
deutscher Volksglaube (Iserlohn, å.d.), p. 34.
E. Hoffmann-Krayer, Feste und Bräuche des
Schweizervolkes (Zurich, 1913), p. 163.
E. H. Meyer, Badisches Volksleben (Strasburg, 1900), p.
507.
J. A. E. Köhler, loc. cit. Tacitus tells us that the image of the
goddess Nerthus, her vestments, and chariot were washed
in a certain lake, and that immediately afterwards the
slaves who ministered to the goddess were swallowed by
the lake (Germania, 40). The statement may perhaps be
understood to mean that the slaves were drowned as a
sacrifice to the deity. Certainly we know from Tacitus
(Germania, 9 and 39) that the ancient Germans offered
human sacrifices.
E. Meier, Deutsche Sagen, Sitten und Gebräuche aus
Schwaben (Stuttgart, 1852), p. 429, § 121.

74.
75.
76.
77.
78.
79.
O. Frh. von Reinsberg-Düringsfeld, Fest-Kalender aus
Böhmen (Prague, å.d.), p. 311.
Karl Lynker, Deutsche Sagen und Sitten in hessischen
Gauen
2
(Cassel and Göttingen, 1860), pp. 253, 254, §§
335, 336.
E. H. Meyer, Badisches Volksleben (Strasburg, 1900), p.
506.
Giuseppe Pitrè, Spettacoli e Feste Popolari Siciliane
(Palermo, 1881), p. 313.
J. Grimm, Deutsche Mythologie,
4
i. 489 sq., iii. 487; A.
Wuttke, Der deutsche Volksaberglaube
2
(Berlin, 1869), p.
77 § 92; O. Freiherr von Reinsberg-Düringsfeld, Das
festliche Jahr (Leipsic, 1863), p. 193; F. J. Vonbun, Beiträge
zur deutschen Mythologie (Chur, 1862), p. 133; P. Drechsler,
Sitte, Brauch und Volksglaube in Schlesien (Leipsic, 1903-
1906), i. 143 § 161; Karl Haupt, Sagenbuch der Lausitz
(Leipsic, 1862-1863), i. 248, No. 303; F. J. Wiedemann, Aus
dem inneren und äusseren Leben der Ehsten (St.
Petersburg, 1876), p. 415; L. Lloyd, Peasant Life in Sweden
(London, 1870), pp. 261 sq.; Paul Sébillot, Le Folk-lore de
France (Paris, 1904-1907), ii. 160 sq.; T. F. Thiselton Dyer,
British Popular Customs (London, 1876), pp. 322 sq., 329
sq. For more evidence, see above, vol. i. pp. 193, 194, 205
sq., 208, 210, 216; Adonis, Attis, Osiris, Second Edition, pp.
204 sqq.
Le Baron de Reinsberg-Düringsfeld, Calendrier Belge
(Brussels, 1861-1862), i. 420 sq.; E. Monseur, Le Folklore
Wallon (Brussels, å.d.), p. 130; P. Sébillot, Le Folk-lore de
France, ii. 374 sq.
E. Hoffmann-Krayer, Feste und Bräuche des
Schweizervolkes (Zurich, 1913), p. 163. See above, p. 27.

80.
81.
82.
83.
84.
85.
86.
87.
E. Westermarck, “Midsummer Customs in Morocco,” Folk-
lore, xvi. (1905) pp. 31 sq.; id., Ceremonies and Beliefs
connected with Agriculture, certain Dates of the Solar Year,
and the Weather in Morocco (Helsingfors, 1913), pp. 84-86;
E. Doutté, Magie et Religion dans l'Afrique du Nord (Algiers,
1908), pp. 567 sq. See also above, vol. i. p. 216.
See above, vol. i. pp. 213-219.
E. Westermarck, Ceremonies and Beliefs connected with
Agriculture, certain Dates of the Solar Year, and the
Weather in Morocco (Helsingfors, 1913), pp. 94 sq.
This has been rightly pointed out by Dr. Edward
Westermarck (“Midsummer Customs in Morocco,” Folk-lore,
xvi. (1905) p. 46).
Caesar, Bell. Gall. vi. 15; Strabo, iv. 4. 5, p. 198; Diodorus
Siculus, v. 32. See W. Mannhardt, Baumkultus, pp. 525 sqq.
Strabo, iv. 4. 4, p. 197: τὰς δὲ φονικὰς δίκας μάλιστα
τούτοις [i.e. the Druids] ἐπετέτραπτο δικάζειν, ὅταν τε
φορὰ τούτων ᾖ, φορὰν καὶ τῆς χώρας νομίζουσιν ὑπάρχειν.
On this passage see W. Mannhardt, Baumkultus, pp. 529
sqq.; and below, pp. 42 sq.
The Magic Art and the Evolution of Kings, ii. 80 sqq.
Madame Clément, Histoire des fêtes civiles et religieuses du
département du Nord
2
(Cambrai, 1836), pp. 193-200; A. de
Nore, Coutumes, Mythes et Traditions des Provinces de
France, (Paris and Lyons, 1846), pp. 323 sq.; F. W. Fairholt,
Gog and Magog, the Giants in Guildhall, their real and
legendary History (London, 1859), pp. 78-87; W.
Mannhardt, Baumkultus, p. 523, note. It is said that the
giantess made her first appearance in 1665, and that the
children were not added to the show till the end of the
seventeenth century. In the eighteenth century the
procession took place on the third Sunday in June, which

88.
89.
90.
91.
must always have been within about a week of Midsummer
Day (H. Gaidoz, “Le dieu gaulois du soleil et le symbolisme
de la roue,” Revue Archéologique, iii. série iv. 32 sq.).
The Gentleman's Magazine, xxix. (1759), pp. 263-265;
Madame Clément, Histoire des fêtes civiles et religieuses du
département du Nord,
2
pp. 169-175; A. de Nore,
Coutumes, Mythes et Traditions des Provinces de France,
pp. 328-332. Compare John Milner, The History, Civil and
Ecclesiastical, and Survey of the Antiquities of Winchester
(Winchester, å.d.), i. 8 sq. note 6; John Brand, Popular
Antiquities of Great Britain (London, 1882-1883), i. 325 sq.;
James Logan, The Scottish Gael or Celtic Manners, edited
by Rev. Alex. Stewart (Inverness, å.d.), ii. 358. According to
the writer in The Gentleman's Magazine the name of the
procession was the Cor-mass.
Madame Clément, Histoire des fêtes civiles et religieuses,
etc., de la Belgique méridionale, etc. (Avesnes, 1846), p.
252; Le Baron de Reinsberg-Düringsfeld, Calendrier Belge
(Brussels, 1861-1862), i. 123-126. We may conjecture that
the Flemish Reuze, like the Reuss of Dunkirk, is only
another form of the German Riese, “giant.”
F. W. Fairholt, Gog and Magog, the Giants in Guildhall, their
real and legendary History (London, 1859), pp. 64-78. For
the loan of this work and of the one cited in the next note I
have to thank Mrs. Wherry, of St. Peter's Terrace,
Cambridge.
E. Fourdin, “La foire d'Ath,” Annales du Cercle
Archéologique de Mons, ix. (Mons, 1869) pp. 7, 8, 12, 36
sq. The history of the festival has been carefully
investigated, with the help of documents by M. Fourdin.
According to him, the procession was religious in its origin
and took its rise from a pestilence which desolated Hainaut
in 1215 (op. cit. pp. 1 sqq.). He thinks that the effigies of

92.
93.
94.
95.
96.
97.
98.
99.
giants were not introduced into the procession till between
1450 and 1460 (op. cit. p. 8).
George Puttenham, The Arte of English Poesie (London,
1811, reprint of the original edition of London, 1589), book
iii. chapter vi. p. 128. On the history of the English giants
and their relation to those of the continent, see F. W.
Fairholt, Gog and Magog, the Giants in Guildhall, their real
and legendary History (London, 1859).
Joseph Strutt, The Sports and Pastimes of the People of
England, New Edition, by W. Hone (London, 1834), pp.
xliii.-xlv.; F. W. Fairholt, Gog and Magog, the Giants in
Guildhall (London, 1859), pp. 52-59.
F. W. Fairholt, op. cit. pp. 59-61.
F. W. Fairholt, op. cit. pp. 61-63.
Felix Liebrecht, Des Gervasius von Tilbury Otia Imperialia
(Hanover, 1856), pp. 212 sq.; A. de Nore, Coutumes,
Mythes, et Traditions des Provinces de France, pp. 354 sq.;
W. Mannhardt, Baumkultus, p. 514.
W. Mannhardt, Baumkultus, pp. 514, 523.
Athenaeum, 24th July 1869, p. 115; W. Mannhardt,
Baumkultus, pp. 515 sq. From a later account we learn that
about the year 1890 the custom of lighting a bonfire and
dancing round it was still observed at Bagnères de Luchon
on Midsummer Eve, but the practice of burning live
serpents in it had been discontinued. The fire was kindled
by a priest. See Folk-lore, xii. (1901) pp. 315-317.
A. Breuil, “Du culte de St.-Jean Baptiste,” Mémoires de la
Société des Antiquaires de Picardie, viii. (1845) pp. 187 sq.;
Collin de Plancy, Dictionnaire Infernal (Paris, 1825-1826), iii.
40; A. de Nore, Coutumes, Mythes et Traditions des
Provinces de France, pp. 355 sq.; J. W. Wolf, Beiträge zur
deutschen Mythologie (Göttingen and Leipsic, 1852-1857),

100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
ii. 388; E. Cortet, Essai sur les Fêtes Religieuses (Paris,
1867), pp. 213 sq.; Laisnel de la Salle, Croyances et
Légendes du Centre de la France (Paris, 1875), i. 82; W.
Mannhardt, Baumkultus, p. 515.
Tessier, in Mémoires et Dissertations publiés par la Société
Royale des Antiquaires de France, v. (1823) p. 388; W.
Mannhardt, Baumkultus, p. 515.
Alexandre Bertrand, La Religion des Gaulois (Paris, 1897),
p. 407.
J. Grimm, Deutsche Mythologie,
4
i. 519; W. Mannhardt,
Baumkultus, p. 515.
W. Mannhardt, Baumkultus, p. 515; Montanus, Die
deutschen Volksfesten, Volksbräuche und deutscher
Volksglaube (Iserlohn, å.d.), p. 34.
W. Mannhardt, Baumkultus, p. 515.
A. Meyrac, Traditions, Coutumes, Légendes, et Contes des
Ardenness (Charleville, 1890), p. 68.
Above, vol. i. p. 142.
Strabo, iv. 4. 5, p. 198, καὶ ἄλλα δὲ ἀνθρωποθυσιῶν εἴδη
λέγεται; καὶ γὰρ κατετόξευόν τινας καὶ ἀνεσταύρουν ἐν τοῖς
ἱεροῖς καὶ κατασκευάσαντες κολοσσὸν χόρτου καὶ ξύλων,
ἐμβαλόντες εἰς τοῦτον βοσκήματα καὶ θηρία παντοῖα καὶ
ἀνθρώπους ὡλοκαύτουν.
Above, p. 39.
Marie Trevelyan, Folk-lore and Folk-stories of Wales
(London, 1909), pp. 214, 301 sq.; Ulrich Jahn, Hexenwesen
und Zauberei in Pommern (Breslau, 1886), p. 7; id.,
Volkssagen aus Pommern und Rügen (Stettin, 1886), p.
353, No. 446.
See above, vol. i. p. 315 n. 1.

111.
112.
113.
114.
115.
The treatment of magic and witchcraft by the Christian
Church is described by W. E. H. Lecky, History of the Rise
and Influence of the Spirit of Rationalism in Europe, New
Edition (London, 1882), i. 1 sqq. Four hundred witches
were burned at one time in the great square of Toulouse
(W. E. H. Lecky, op. cit. ii. 38). Writing at the beginning of
the eighteenth century Addison observes: “Before I leave
Switzerland I cannot but observe, that the notion of
witchcraft reigns very much in this country. I have often
been tired with accounts of this nature from very sensible
men, who are most of them furnished with matters of fact
which have happened, as they pretend, within the compass
of their own knowledge. It is certain there have been many
executions on this account, as in the canton of Berne there
were some put to death during my stay at Geneva. The
people are so universally infatuated with the notion, that if
a cow falls sick, it is ten to one but an old woman is clapt
up in prison for it, and if the poor creature chance to think
herself a witch, the whole country is for hanging her up
without mercy.” See The Works of Joseph Addison, with
notes by R. Hurd, D.D. (London, 1811), vol. ii., “Remarks on
several Parts of Italy,” p. 196.
Strabo, iv. 4. 4, p. 197. See the passage quoted above, p.
32, note 2.
W. Mannhardt, Baumkultus, pp. 532-534.
Spirits of the Corn and of the Wild, i. 270-305.
Some of the serpents worshipped by the old Prussians lived
in hollow oaks, and as oaks were sacred among the
Prussians, the serpents may possibly have been regarded
as genii of the trees. See Simon Grunau, Preussischer
Chronik, herausgegeben von Dr. M. Perlbach, i. (Leipsic,
1876) p. 89; Christophor Hartknoch, Alt und Neues
Preussen (Frankfort and Leipsic, 1684), pp. 143, 163.
Serpents played an important part in the worship of

116.
117.
118.
119.
Demeter, but we can hardly assume that they were
regarded as embodiments of the goddess. See Spirits of the
Corn and of the Wild, ii. 17 sq.
For example, in China the spirits of plants are thought to
assume the form of snakes oftener than that of any other
animal. Chinese literature abounds with stories illustrative
of such transformations. See J. J. M. de Groot, The
Religious System of China, iv. (Leyden, 1901) pp. 283-286.
In Siam the spirit of the takhien tree is said to appear
sometimes in the shape of a serpent and sometimes in that
of a woman. See Adolph Bastian, Die Voelker des
Oestlichen Asien, iii. (Jena, 1867) p. 251. The vipers that
haunted the balsam trees in Arabia were regarded by the
Arabs as sacred to the trees (Pausanias, ix. 28. 4); and
once in Arabia, when a wood hitherto untouched by man
was burned down to make room for the plough, certain
white snakes flew out of it with loud lamentations. No
doubt they were supposed to be the dispossessed spirits of
the trees. See J. Wellhausen, Reste Arabischen
Heidentums
2
(Berlin, 1897), pp. 108 sq.
J. L. M. Noguès, Les mœurs d'autrefois en Saintonge et en
Aunis (Saintes, 1891), p. 71. Amongst the superstitious
practices denounced by the French writer J. B. Thiers in the
seventeenth century was “the gathering of certain herbs
between the Eve of St. John and the Eve of St. Peter and
keeping them in a bottle to heal certain maladies.” See J. B.
Thiers, Traité des Superstitions (Paris, 1679), p. 321.
A. de Nore, Coutumes, Mythes et Traditions des Provinces
de France (Paris and Lyons, 1846), pp. 150 sq.
Jules Lecœur, Esquisses du Bocage Normand (Condé-sur-
Noireau, 1883-1887), ii. 8, 244; Amélie Bosquet, La
Normandie romanesque et merveilleuse (Paris and Rouen,
1845), p. 294.

120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
De la Loubere, Du Royaume de Siam (Amsterdam, 1691), i.
202. The writer here mentions an Italian mode of divination
practised on Midsummer Eve. People washed their feet in
wine and threw the wine out of the window. After that, the
first words they heard spoken by passers-by were deemed
oracular.
Aubin-Louis Millin, Voyage dans les Départements du Midi
de la France (Paris, 1807-1811), iii. 344 sq.
Alexandre Bertrand, La Religion des Gaulois (Paris, 1897),
p. 124. In French the name of St. John's herb (herbe de la
Saint-Jean) is usually given to millepertius, that is, St.
John's wort, which is quite a different flower. See below,
pp. 54 sqq. But “St. John's herb” may well be a general
term which in different places is applied to different plants.
Bruno Stehle, “Aberglauben, Sitten und Gebräuche in
Lothringen,” Globus, lix. (1891) p. 379.
L. F. Sauvé, Le Folk-lore des Hautes-Vosges (Paris, 1889),
pp. 168 sq.
I. V. Zingerle, “Wald, Bäume, Kräuter,” Zeitschrift für
deutsche Mythologie und Sittenkunde, i. (1853) pp. 332
sq.; id., Sitten, Bräuche und Meinungen des Tiroler Volkes
2
(Innsbruck, 1871), p. 158, §§ 1345, 1348.
Christian Schneller, Märchen und Sagen aus Wälschtirol
(Innsbruck, 1867), p. 237, § 24.
J. H. Schmitz, Sitten und Bräuche, Lieder, Sprüchwörter und
Räthsel des Eifler Volkes (Treves, 1856-1858), i. 40.
J. H. Schmitz, op. cit. i. 42.
A. Kuhn, Märkische Sagen und Märchen (Berlin, 1843), p.
330.
K. Bartsch, Sagen, Märchen und Gebräuche aus
Mecklenburg (Vienna, 1879-1880), ii. p. 287, § 1436.

131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
W. von Schulenburg, Wendische Volkssagen und Gebräuche
aus dem Spreewald (Leipsic, 1880), p. 254.
M. Prätorius, Deliciae Prussicae (Berlin, 1871), pp. 24 sq.
Kaupole is probably identical in name with Kupole or
Kupalo, as to whom see The Dying God, pp. 261 sq.
Alois John, Sitte, Brauch und Volksglaube im deutschen
Westböhmen (Prague, 1905), p. 86.
R. F. Kaindl, Die Huzulen (Vienna, 1894), pp. 78, 90, 93,
105; id., “Zauberglaube bei den Huzulen,” Globus, lxxvi.
(1899) p. 256.
Dr. F. Tetzner, “Die Tschechen und Mährer in Schlesien,”
Globus, lxxviii. (1900) p. 340.
J. B. Holzmayer, “Osiliana,” Verhandlungen der gelehrten
Estnischen Gesellschaft, vii. Heft 2 (Dorpat, 1872), p. 62.
P. Einhorn, “Wiederlegunge der Abgötterey: der ander (sic)
Theil,” printed at Riga in 1627, and reprinted in Scriptores
rerum Livonicarum, ii. (Riga and Leipsic, 1848) pp. 651 sq.
J. G. Kohl, Die deutsch-russischen Ostseeprovinzen
(Dresden and Leipsic, 1841), ii. 26.
A. Strausz, Die Bulgaren (Leipsic, 1898), pp. 348, 386.
F. S. Krauss, Volksglaube und religiöser Brauch der
Südslaven (Münster i. W., 1890), p. 34.
G. F. Abbott, Macedonian Folk-lore (Cambridge, 1903), pp.
54, 58.
H. A. Weddell, Voyage dans le Nord de la Bolivie et dans les
parties voisines du Pérou (Paris and London, 1853), p. 181.
W. Westermarck, “Midsummer Customs in Morocco,” Folk-
lore, xvi. (1905) p. 35; id., Ceremonies and Beliefs
connected with Agriculture, certain Dates of the Solar Year,
and the Weather in Morocco (Helsingfors, 1913), pp. 88 sq.

144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.
160.
J. Lecœur, Esquisses du Bocage Normand (Condé-sur-
Noireau, 1883-1887), ii. 9.
K. Bartsch, Sagen, Märchen und Gebräuche aus
Mecklenburg (Vienna, 1879-1890), ii. 285.
J. A. E. Köhler, Volksbrauch, Aberglauben, Sagen und andre
alte Ueberlieferungen im Voigtlande (Leipsic, 1867), p. 376.
O. Freiherr von Reinsberg-Düringsfeld, Fest-Kalender aus
Böhmen (Prague, å.d.), p. 312.
Reinsberg-Düringsfeld, loc. cit.
M. Töppen, Aberglauben aus Masuren
2
(Danzig, 1867), p.
72.
Reinsberg-Düringsfeld, loc. cit.
J. A. E. Köhler, Volksbrauch, etc., im Voigtlande, p. 376.
C. Lemke, Volksthümliches in Ostpreussen (Mohrungen,
1884-1887), i. 20.
P. Drechsler, Sitte, Brauch und Volksglaube in Schlesien
(Leipsic, 1903-1906), i. 144 sq.
Le Baron de Reinsberg-Düringsfeld, Calendrier Belge
(Brussels, 1861-1862), i. 423.
Marie Trevelyan, Folk-lore and Folk-stories of Wales
(London, 1909), p. 252.
M. Töppen, Aberglauben aus Masuren,
2
p. 72.
M. Töppen, op. cit. p. 71.
A. Wiedemann, Aus dem inneren und äussern Leben der
Ehsten (St. Petersburg, 1876), pp. 362 sq.
L. Lloyd, Peasant Life in Sweden (London, 1870), pp. 267
sq.

161.
162.
163.
Willibald Müller, Beiträge zur Volkskunde der Deutschen in
Mähren (Vienna and Olmütz, 1893), p. 264.
W. von Schulenburg, Wendisches Volksthum (Berlin, 1882),
p. 145.
Montanus, Die deutschen Volksfeste, Volksbräuche und
deutscher Volksglaube (Iserlohn, å.d.), p. 145; A. Wuttke,
Der deutsche Volksaberglaube
2
(Berlin, 1869), p. 100, §
134; I. V. Zingerle, “Wald, Bäume, Kräuter,” Zeitschrift für
deutsche Mythologie und Sittenkunde, i. (1853) p. 329; A.
Schlossar, “Volksmeinung und Volksaberglaube aus der
deutschen Steiermark,” Germania, N.R., xxiv. (1891) p. 387;
E. Meier, Deutsche Sagen, Sitten und Gebräuche aus
Schwaben (Stuttgart, 1852), p. 428; J. Brand, Popular
Antiquities of Great Britain (London, 1882-1883), i. 307,
312; T. F. Thiselton Dyer, Folk-lore of Plants (London, 1889),
pp. 62, 286; Rev. Hilderic Friend, Flowers and Flower Lore,
Third Edition (London, 1886), pp. 147, 149, 150, 540; G.
Finamore, Credenze, Usi e Costumi Abruzzesi (Palermo,
1890), pp. 161 sq.; G. Pitrè, Spettacoli e Feste Popolari
Siciliane (Palermo, 1881), p. 309. One authority lays down
the rule that you should gather the plant fasting and in
silence (J. Brand, op. cit. p. 312). According to Sowerby,
the Hypericum perforatum flowers in England about July
and August (English Botany, vol. v. London, 1796, p. 295).
We should remember, however, that in the old calendar
Midsummer Day fell twelve days later than at present. The
reform of the calendar probably put many old floral
superstitions out of joint.
Bingley, Tour round North Wales (1800), ii. 237, quoted by
T. F. Thiselton Dyer, British Popular Customs (London,
1876), p. 320. Compare Marie Trevelyan, Folk-lore and Folk-
stories of Wales (London, 1909), p. 251: “St. John's, or
Midsummer Day, was an important festival. St. John's wort,
gathered at noon on that day, was considered good for

164.
165.
166.
167.
168.
169.
170.
171.
172.
several complaints. The old saying went that if anybody
dug the devil's bit at midnight on the eve of St. John, the
roots were then good for driving the devil and witches
away.” Apparently by “the devil's bit” we are to understand
St. John's wort.
J. L. M. Noguès, Les mœurs d'autrefois en Saintonge et en
Aunis (Saintes, 1891), pp. 71 sq.
Alois John, Sitte, Brauch und Volksglaube im deutschen
Westböhmen (Prague, 1905), p. 84. They call the plant
“witch's herb” (Hexenkraut).
James Sowerby, English Botany, vol. v. (London, 1796), p.
295.
Montanus, Die deutschen Volksfeste, Volksbräuche und
deutscher Volksglaube (Iserlohn, å.d.), p. 35.
T. F. Thiselton Dyer, Folk-lore of Plants (London, 1889), p.
286; K. Bartsch, Sagen, Märchen und Gebräuche aus
Mecklenburg, ii. p. 291, § 1450a. The Germans of Bohemia
ascribe wonderful virtues to the red juice extracted from
the yellow flowers of St. John's wort (W. Müller, Beiträge
zur Volkskunde der Deutschen in Mähren, Vienna and
Olmütz, 1893, p. 264).
K. Bartsch, op. cit. ii. p. 286, § 1433. The blood is also a
preservative against many diseases (op. cit. ii. p. 290, §
1444).
A. Kuhn, Märkische Sagen und Märchen (Berlin, 1843), p.
387, § 105.
Die gestriegelte Rockenphilosophie
5
(Chemnitz, 1759), pp.
246 sq.; Montanus, Die deutschen Volksfesten,
Volksbräuche und deutscher Volksglaube, p. 147.
Berthold Seeman, Viti, An Account of a Government Mission
to the Vitian or Fijian Islands in the years 1860-61

173.
174.
175.
176.
177.
178.
179.
180.
(Cambridge, 1862), p. 63.
James Sowerby, English Botany, vol. xvi. (London, 1803) p.
1093.
K. Seifart, Sagen, Märchen, Schwänke und Gebräuche aus
Stadt und Stift Hildesheim
2
(Hildesheim, 1889), p. 177, §
12.
C. L. Rochholz, Deutscher Glaube und Brauch (Berlin,
1867), i. 9.
J. V. Grohmann, Aberglauben und Gebräuche aus Böhmen
und Mähren (Prague and Leipsic, 1864), p. 98, § 681.
A. Wuttke, Der deutsche Volksaberglaube
2
(Berlin, 1869),
p. 100, § 134.
J. A. E. Köhler, Volksbrauch, Aberglauben, Sagen und andre
alte Ueberlieferungen im Voigtlande (Leipsic, 1867), p. 376.
The belief and practice are similar at Grün, near Asch, in
Western Bohemia. See Alois John, Sitte, Brauch und
Volksglaube im deutschen Westböhmen (Prague, 1905), p.
84.
F. Panzer, Beitrag zur deutschen Mythologie (Munich, 1848-
1855), ii. 299; Bavaria, Landes- und Volkskunde des
Königreichs Bayern, iii. (Munich, 1865), p. 342; I. V.
Zingerle, Sitten, Bräuche und Meinungen des Tiroler
Volkes
2
(Innsbruck, 1871), p. 160, § 1363.
J. Grimm, Deutsche Mythologie,
4
ii. 1013; A. de Gubernatis,
Mythologie des Plantes (Paris, 1878-1882), i. 189 sq.; Rev.
Hilderic Friend, Flowers and Flower Lore, Third Edition
(London, 1886), p. 75. In England mugwort is very
common in waste ground, hedges, and the borders of
fields. It flowers throughout August and later. The root is
woody and perennial. The smooth stems, three or four feet
high, are erect, branched, and leafy, and marked by many

181.
182.
183.
184.
longitudinal purplish ribs. The pinnatified leaves alternate
on the stalk; they are smooth and dark green above,
cottony and very white below. The flowers are in simple
leafy spikes or clusters; the florets are purplish, furnished
with five stamens and five awl-shaped female flowers,
which constitute the radius. The whole plant has a weak
aromatic scent and a slightly bitter flavour. Its medical
virtues are of no importance. See James Sowerby, English
Botany, xiv. (London, 1802) p. 978. Altogether it is not easy
to see why such an inconspicuous and insignificant flower
should play so large a part in popular superstition. Mugwort
(Artemisia vulgaris) is not to be confounded with
wormwood (Artemisia absinthium), which is quite a
different flower in appearance, though it belongs to the
same genus. Wormwood is common in England, flowering
about August. The flowers are in clusters, each of them
broad, hemispherical, and drooping, with a buff-coloured
disc. The whole plant is of a pale whitish green and clothed
with a short silky down. It is remarkable for its intense
bitterness united to a peculiar strong aromatic odour. It is
often used to keep insects from clothes and furniture, and
as a medicine is one of the most active bitters. See James
Sowerby, English Botany, vol. xviii. (London, 1804) p. 1230.
Breuil, “Du culte de St.-Jean-Baptiste,” Mémoires de la
Société des Antiquaires de Picardie, viii. (1845) p. 224, note
1, quoting the curé of Manancourt, near Péronne.
L. Pineau, Le folk-lore du Poitou (Paris, 1892), p. 499.
J. V. Grohmann, Aberglauben und Gebräuche aus Böhmen
und Mähren (Prague and Leipsic, 1864), pp. 90 sq., §§ 635-
637.
F. Panzer, Beitrag zur deutschen Mythologie, i. p. 249, §
283; J. Grimm, Deutsche Mythologie,
4
ii. 1013; I. V.
Zingerle, in Zeitschrift für deutsche Mythologie und

185.
186.
187.
188.
189.
190.
191.
192.
193.
194.
195.
196.
197.
Sittenkunde, i. (1853) p. 331. and ib. iv. (1859) p. 42
(quoting a work of the seventeenth century); F. J. Vonbun,
Beiträge zur deutschen Mythologie (Chur, 1862), p. 133,
note 1. See also above, vol. i. pp. 162, 163, 165, 174, 177.
A. de Gubernatis, Mythologie der Plantes (Paris, 1878-
1882), i. 190, quoting Du Cange.
A. de Nore, Coutumes, Mythes et Traditions des Provinces
de France (Paris and Lyons, 1846), p. 262.
Jules Lecœur, Esquisses du Bocage Normand (Condé-sur-
Noireau, 1883-1886), ii. 8.
Joseph Train, Historical and Statistical Account of the Isle of
Man (Douglas, Isle of Man, 1845), ii. 120.
Le Baron de Reinsberg-Düringsfeld, Calendrier Belge
(Brussels, 1861-1862), i. 422.
J. J. M. de Groot, The Religious System of China, vi.
(Leyden, 1910) p. 1079, compare p. 947.
J. J. M. de Groot, op. cit. vi. 947.
J. J. M. de Groot, op. cit. vi. 946 sq.
Rev. John Batchelor, The Ainu and their Folk-lore (London,
1901), p. 318, compare pp. 315 sq., 329, 370, 372.
Zeitschrift für deutsche Mythologie und Sittenkunde, iv.
(1859) p. 42; Montanus, Die deutschen Volksfeste, p. 141.
The German name of mugwort (Beifuss) is said to be
derived from this superstition.
K. Bartsch, Sagen, Märchen, und Gebräuche aus
Mecklenburg (Vienna, 1879-1880), ii. 290, § 1445.
Montanus, Die deutschen Volksfeste, p. 141.
J. Brand, Popular Antiquities of Great Britain (London,
1882-1883), i. 334 sq., quoting Lupton, Thomas Hill, and
Paul Barbette. A precisely similar belief is recorded with

198.
199.
200.
201.
regard to wormwood (armoise) by the French writer J. B.
Thiers, who adds that only small children and virgins could
find the wonderful coal. See J. B. Thiers, Traité des
Superstitions
5
(Paris, 1741), i. 300. In Annam people think
that wormwood puts demons to flight; hence they hang up
bunches of its leaves in their houses at the New Year. See
Paul Giran, Magie et Religion Annamites (Paris, 1912), p.
118, compare pp. 185, 256.
C. Lemke, Volksthümliches in Ostpreussen (Mohrungen,
1884-1887), i. 21. As to mugwort (German Beifuss, French
armoise), see further A. de Gubernatis, Mythologie des
Plantes, ii. 16 sqq.; J. Grimm, Deutsche Mythologie,
4
iii.
356 sq.
James Sowerby, English Botany, vol. xix. (London, 1804) p.
1319.
John Aubrey, Remains of Gentilisme and Judaisme (London,
1881), pp. 25 sq.; J. Brand, Popular Antiquities of Great
Britain (London, 1882-1883), i. 329 sqq.; Rev. Hilderic
Friend, Flowers and Flower Lore, Third Edition (London,
1886), p. 136; D. H. Moutray Read, “Hampshire Folk-lore,”
Folk-lore, xxii. (1911) p. 325. Compare J. Sowerby, English
Botany, vol. xix. (London, 1804), p. 1319: “Like all
succulent plants this is very tenacious of life, and will keep
growing long after it has been torn from its native spot.
The country people in Norfolk sometimes hang it up in their
cottages, judging by its vigour of the health of some absent
friend.” It seems that in England the course of love has
sometimes been divined by means of sprigs of red sage
placed in a basin of rose-water on Midsummer Eve (J.
Brand, op. cit. i. 333).
M. Töppen, Aberglauben aus Masuren
2
(Danzig, 1867), pp.
71 sq.; A. Kuhn, Sagen, Gebräuche und Märchen aus
Westfalen (Leipsic, 1859), ii. 176, § 487; E. Hoffmann-

202.
203.
204.
205.
206.
Krayer, Feste und Bräuche des Schweizervolkes (Zurich,
1913), p. 163. In Switzerland the species employed for this
purpose on Midsummer day is Sedum reflexum. The
custom is reported from the Emmenthal. In Germany a root
of orpine, dug up on St. John's morning and hung between
the shoulders, is sometimes thought to be a cure for
hemorrhoids (Montanus, Die deutschen Volksfeste, p. 145).
Perhaps the “oblong, tapering, fleshy, white lumps” of the
roots (J. Sowerby, English Botany, vol. xix. London, 1804,
p. 1319) are thought to bear some likeness to the
hemorrhoids, and to heal them on the principle that the
remedy should resemble the disease.
See above, vol. i. pp. 162, 163, 165. In England vervain
(Verbena officinalis) grows not uncommonly by road sides,
in dry sunny pastures, and in waste places about villages. It
flowers in July. The flowers are small and sessile, the
corolla of a very pale lilac hue, its tube enclosing the four
short curved stamens. The root of the plant, worn by a
string round the neck, is an old superstitious medicine for
scrofulous disorders. See James Sowerby, English Botany,
vol. xi. (London, 1800) p. 767.
Dr. Otero Acevado, in Le Temps, September 1898. See
above, vol. i. p. 208, note 1.
Le Baron de Reinsberg-Düringsfeld, Calendrier Belge
(Brussels, 1861-1862), i. 422.
A. de Nore, Coutumes, Mythes et Traditions des Provinces
de France, p. 262; Amélie Bosquet, La Normandie
romanesque et merveilleuse, p. 294; J. Lecœur, Esquisses
du Bocage Normand, i. 287, ii. 8. In Saintonge and Aunis
the plant was gathered on Midsummer Eve for the purpose
of evoking or exorcising spirits (J. L. M. Noguès, Les mœurs
d'autrefois en Saintonge et en Aunis, p. 72).

207.
208.
209.
210.
211.
212.
213.
214.
215.
J. V. Grohmann, Aberglauben und Gebräuche aus Böhmen
und Mähren, p. 207, § 1437.
A. Kuhn, Sagen, Gebräuche und Märchen aus Westfalen
(Leipsic, 1859), ii. 177, citing Chambers, Edinburgh Journal,
2nd July 1842.
I. V. Zingerle, Sitten, Bräuche und Meinungen des Tiroler
Volkes
2
(Innsbruck, 1871), p. 107, § 919.
Laisnel de la Salle, Croyances et Légendes du Centre de la
France (Paris, 1875), i. 288.
J. L. M. Noguès, Les mœurs d'autrefois en Saintonge et en
Aunis, pp. 71 sq.
Le Baron de Reinsberg-Düringsfeld, Calendrier Belge, i.
423.
W. Kolbe, Hessische Volks-Sitten und Gebräuche
2
(Marburg,
1888), p. 72; Sophus Bugge, Studien über die Entstehung
der nordischen Götter- und Heldensagen (Munich, 1889),
pp. 35, 295 sq.; Fr. Kauffmann, Balder (Strasburg, 1902),
pp. 45, 61. The flowers of common camomile (Anthemis
nobilis) are white with a yellow disk, which in time becomes
conical. The whole plant is intensely bitter, with a peculiar
but agreeable smell. As a medicine it is useful for stomachic
troubles. In England it does not generally grow wild. See
James Sowerby, English Botany, vol. xiv. (London, 1802) p.
980.
A. Kuhn, Sagen, Gebräuche und Märchen aus Westfalen
(Leipsic, 1859), ii. 177, § 488.
M. Töppen, Aberglauben aus Masuren
2
(Danzig, 1867), p.
71.
A. Witzschel, Sagen, Sitten und Gebräuche aus Thüringen
(Vienna, 1878), p. 289, § 139.

216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
W. J. A. von Tettau und J. D. H. Temme, Volkssagen
Ostpreussens, Litthauens und Westpreussens (Berlin,
1837), p. 283.
James Sowerby, English Botany, vol. vii. (London, 1798), p.
487. As to great mullein or high taper, see id., vol. viii.
(London, 1799), p. 549.
Tettau und Temme, loc. cit. As to mullein at Midsummer,
see also above, vol. i. pp. 190, 191.
J. V. Grohmann, Aberglauben und Gebräuche aus Böhmen
und Mähren, p. 205, § 1426.
J. V. Grohmann, op. cit. p. 93, § 648.
J. A. E. Köhler, Volksbrauch, Aberglauben, Sagen und andre
alte Ueberlieferungen im Voigtlande (Leipsic, 1867), p. 377.
Alois John, Sitte, Brauch und Volksglaube im deutschen
Westböhmen (Prague, 1905), p. 84.
J. N. Ritter von Alpenburg, Mythen und Sagen Tirols
(Zurich, 1857), p. 397.
C. Russwurm, “Aberglaube aus Russland,” Zeitschrift für
deutsche Mythologie und Sittenkunde, iv. (1859) pp. 153
sq. The purple loosestrife is one of our most showy English
wild plants. In July and August it may be seen flowering on
the banks of rivers, ponds, and ditches. The separate
flowers are in axillary whorls, which together form a loose
spike of a reddish variable purple. See James Sowerby,
English Botany, vol. xv. (London, 1802) p. 1061.
J. Brand, Popular Antiquities, i. 314 sqq.; Hilderic Friend,
Flowers and Flower Lore, Third Edition (London, 1886), pp.
60, 78, 150, 279-283; Miss C. S. Burne and Miss G. F.
Jackson, Shropshire Folk-lore (London, 1883), p. 242; Marie
Trevelyan, Folk-lore and Folk-stories of Wales (London,
1909), pp. 89 sq.; J. B. Thiers, Traité des Superstitions

(Paris, 1679), p. 314; J. Lecœur, Esquisses du Bocage
Normand, i. 290; P. Sébillot, Coutumes populaires de la
Haute-Bretagne (Paris, 1886), p. 217; id., Traditions et
Superstitions de la Haute-Bretagne (Paris, 1882), ii. 336; A.
Wuttke, Der deutsche Volksaberglaube
2
(Berlin, 1869), pp.
94 sq., § 123; F. J. Vonbun, Beiträge zur deutschen
Mythologie (Chur, 1862), pp. 133 sqq.; Montanus, Die
deutschen Volksfesten, p. 144; K. Bartsch, Sagen, Märchen
und Gebräuche aus Mecklenburg, ii. 288, § 1437; M.
Töppen, Aberglauben aus Masuren,
2
p. 72; A. Schlossar,
“Volksmeinung und Volksaberglaube aus der deutschen
Steiermark,” Germania, N.R., xxiv. (1891) p. 387; Theodor
Vernaleken, Mythen und Bräuche des Volkes in Oesterreich
(Vienna, 1859), p. 309; J. N. Ritter von Alpenburg, Mythen
und Sagen Tirols (Zurich, 1857), pp. 407 sq.; I. V. Zingerle,
Sitten, Bräuche und Meinungen des Tiroler Volkes
2
(Innsbruck, 1871), p. 103, § 882, p. 158, § 1350; Christian
Schneller, Märchen und Sagen aus Wälschtirol (Innsbruck,
1867), p. 237; J. V. Grohmann, Aberglauben und Gebräuche
aus Böhmen und Mähren, p. 97, §§ 673-677; Reinsberg-
Düringsfeld, Fest-Kalendar aus Böhmen (Prague, å.d.), pp.
311 sq.; W. Müller, Beiträge zur Volkskunde der Deutschen
in Mähren (Vienna and Olmutz, 1893), p. 265; R. F. Kaindl,
Die Huzulen (Vienna, 1894), p. 106; id., “Zauberglaube bei
den Huzulen,” Globus, lxxvi. (1899) p. 275; P. Drechsler,
Sitte, Brauch und Volksglaube in Schlesien (Leipsic, 1903-
1906), i. 142, § 159; G. Finamore, Credenze, Usi e Costumi
Abruzzesi (Palermo, 1890), p. 161; C. Russwurm,
“Aberglaube in Russland,” Zeitschrift für deutsche
Mythologie und Sittenkunde, iv. (1859) pp. 152 sq.; A. de
Gubernatis, Mythologie des Plantes (Paris, 1878-1882), ii.
144 sqq. The practice of gathering ferns or fern seed on the
Eve of St. John was forbidden by the synod of Ferrara in
1612. See J. B. Thiers, Traité des Superstitions
5
(Paris,

226.
227.
228.
229.
230.
231.
232.
1741), i. 299 sq. In a South Slavonian story we read how a
cowherd understood the language of animals, because
fern-seed accidentally fell into his shoe on Midsummer Day
(F. S. Krauss, Sagen und Märchen der Südslaven, Leipsic,
1883-1884, ii. 424 sqq., No. 159). On this subject I may
refer to my article, “The Language of Animals,” The
Archaeological Review, i. (1888) pp. 164 sqq.
J. V. Grohmann, op. cit. p. 97, §§ 673, 675.
Zeitschrift für deutsche Mythologie und Sittenkunde, iv.
(1859) pp. 152 sq.; A. de Gubernatis, Mythologie des
Plantes, ii. 146.
M. Longworth Dames and E. Seemann, “Folk-lore of the
Azores,” Folk-lore, xiv. (1903) pp. 142 sq.
August Witzschel, Sagen, Sitten und Gebräuche aus
Thüringen (Vienna, 1878), p. 275, § 82.
W. Müller, Beiträge zur Volkskunde der Deutschen in
Mähren (Vienna and Olmutz, 1893), p. 265; K. Bartsch,
Sagen, Märchen und Gebräuche aus Mecklenburg, ii. p.
285, § 1431, p. 288, § 1439; J. Napier, Folk-lore, or
Superstitious Beliefs in the West of Scotland (Paisley, 1879),
p. 125.
A. Kuhn, Märkische Sagen und Märchen (Berlin, 1843), p.
330. As to the divining-rod in general, see A. Kuhn, Die
Herabkunft des Feuers und des Göttertranks
2
(Gütersloh,
1886), pp. 181 sqq.; J. Grimm, Deutsche Mythologie,
4
ii.
813 sqq.; S. Baring-Gould, Curious Myths of the Middle
Ages (London, 1884), pp. 55 sqq. Kuhn plausibly suggests
that the forked shape of the divining-rod is a rude
representation of the human form. He compares the shape
and magic properties of mandragora.
F. Panzer, Beitrag zur deutschen Mythologie (Munich, 1848-
1855), i. 296 sq.

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