Received: 9 August 2022
Revised: 26 May 2023
Accepted: 22 June 2023
DOI: 10.1002/mp.16604
M E D I C A L P H Y S I C S DATA S E T A R T I C L E
A comprehensive open-access database of electron
backscattering coefficients for energies ranging from
0.1 keV to 15 MeV
Fatemeh Akbari
Department of Radiation Oncology, University
of Toledo Health Science Campus, Toledo,
Ohio, USA
Correspondence
Fatemeh Akbari, 3000 Arlington Avenue,
Toledo, OH 43614, USA.
Email: f.akbari1@gmail.com
Abstract
Purpose: The characterization of electron backscattering is essential in medical physics for accurately assessing dose deposited around inhomogeneities
where backscattering alters the spatial energy distribution pattern and for determining Monte-Carlo code’s ability to effectively describe electron scattering
and does calculation in a target volume. Recent machine learning advances
have provided physicists with powerful tools for effectively extracting information and trends from extensive experiment observations if sufficiently sizeable
datasets are available for data mining. We report on the development of a
publicly accessible database on electron backscattering coefficients for solid
targets.
Acquisition and validation methods: The first database on electron-solid
interactions was assembled in 1995. Data for bulk materials, limited to normal incidence and energies up to 100 keV, were primarily focusing on electron
microscopy. To accommodate broad high-energy applications and include the
most recent publications we have created a comprehensive database of electron backscattering coefficients, listed as a function of target atomic number
and thickness, electron energy, and incidence angle. These additions resulted
in a database of 3566 data points, compared to the previous database of 1430.
The data collection includes only published experimental observations (no calculations or results fitting) with no attempt to judge their accuracy or quality. A
limited number of data points were compared to recently published Monte-Carlo
results.
Data format and usage notes: The presented database provides values of
electron backscattering coefficients for 50 elements and 19 compounds at electron energies ranging from 0.1 keV to 15 MeV, presented in ASCII files. Each file
contains the electron energy and backscattering coefficient with target thickness or electron incidence angle included where available, and the reference
number shown in the last column. Additionally, the presented data were shown
in the graphs for better visualization. The online database can be accessed from
the website https://doi.org/10.5281/zenodo.7810951.
Potential applications: The database provides the most up-to-date source of
experimentally obtained electron backscattering coefficients that can be used in
theoretical and MC calculations and modeling validations.The data availability is
still very limited for many solids and almost non-existent for compounds. Novel
machine learning methods should be well adapted to predict these unknown
values for various targets, thicknesses, energies, and incident angles utilizing
the presented cleaned dataset.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any
medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
© 2023 The Authors. Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.
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wileyonlinelibrary.com/journal/mp
Med Phys. 2023;50:5920–5929.
5921
KEYWORDS
database, electron backscattering, open-access
1
INTRODUCTION
When a primary electron beam is incident on a target material, there is penetration and interaction with
the target’s atoms. The electrons continuously change
their direction of motion due to the elastic scattering
with the targets’ atoms nuclei, whereby they lose part
of their energy due to the inelastic scattering with the
targets’ atom’s electrons. This process is often characterized in terms of the backscattering coefficient (“η” or
“eta”), defined as the ratio of the total electron current
reflected into the hemisphere above the target surface
to the incident electron current.1 These electrons allow
valuable information regarding the characteristics of the
target materials to be collected. These electrons contain variable information regarding the characteristics
of the target materials. There is considerable variation
between the definitions of the parameters used by different researchers to characterize the backscattering of
charged particles. For consistent terminology, we define
E (in keV) as the kinetic energy of the incident monoenergetic charged particle beam. Z is the target’s atomic
number, t is the film thickness, and 0 < = α < 90◦ is the
incidence angle, which is formed by the incident beam’s
vector and the vector perpendicular to the target surface.
Electron backscattering is of great interest in many
applications, such as scanning electron microscopy
(SEM) and image analysis, electron microlithography,
Auger electron spectroscopy, and film thickness determination. This phenomenon is crucial in medical physics
for radiation damage studies and accurately assessing the doses deposited around inhomogeneities where
backscattering alters the spatial energy distribution
pattern.2,3 Investigations in radiotherapy and radiobiology should consider the backscattering of electrons at
interfaces such as tissue-bone, lung-bone, lung-tissue
or air-tissue since it changes dosimetry and causes
overdosing of lower density tissue. The significance
of backscattering while irradiating inhomogeneous tissues during radiotherapy has led to the introduction
of proper corrections in treatment planning systems.4
The backscattering process is involved in the dosage
adjustment from internal shielding with high-Z materials.
For example, using lead or tungsten in electron beam
therapy for lip cancer or superficial lesions like those
of the eyelid, buccal mucosa, and ear. Backscattering
simulations are also a critical framework for determining a Monte Carlo transport code’s ability to effectively
describe electron multiple scattering, which in turn
affects the backscattered fraction, their energy spectrum and angular distribution, and calculated energy
deposition in a target volume.5
In recent decades, many studies have explored the
general tendency of the dependence of the backscattering coefficient on the atomic number of the target and
incident electron energy. It was observed that the high
Z targets exhibit stronger elastic scattering and, correspondingly, more significant deflections, amplifying the
yields of backscattered electrons. The general behavior
of the primary energy dependence of the backscattering coefficient was also found. Since higher energy
electrons are more forward-directed, η decreases as
the incident energy increases. Additionally, electron
backscattering depends on material thickness, reaching a bulk specimen value known as the saturation
thickness, when the layer thickness reaches close to
twice the electron range in the material. It was also
observed that η is surface sensitive, that is, its value
when a thin film is deposited on the top of different materials is different from those in the absence
of the substrate. Furthermore, studies on the orientation dependence of electron backscattering have been
shown that in general, η increases with the angle of the
oblique incident.
Recent machine learning (ML) advances have provided physicists with powerful tools to extract information and trends from extensive simulations or experiment datasets. The power of machine learning has
previously been demonstrated in numerous fields of
materials science, particularly in the prediction of a
variety of material’s mechanical, thermodynamic, and
electrical properties.6–11 Other possible applications for
ML include the prediction of electron inelastic mean
free paths, band gaps in semiconductors, stopping
power predictions, and machine learning on neutron
and x-ray scattering and spectroscopies.12–15 In addition to various investigations in imaging applications,
the ML technique has been of interest to medical
physicists for the prediction of radiation treatment side
effects or patients who would benefit from adaptive
radiotherapy.16–18 However, the lack of sufficiently sizeable datasets for data mining restricts the application
of ML techniques. If publicly open, such data resources
would also enable research by scientists without access
to particular experimental equipment. A database of
measured electron backscattering as a function of the
atomic number of the target and the incident beam
energy has been created by Joy19 for several elements and compounds for low energy electron beams.
This quantity, however, varies greatly depending on the
electron incidence angle and target thickness. Additionally, missing higher energy data can be critical for
various spectroscopy applications and the measurement of radiation fields in radiotherapy. Unfortunately,
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ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
there appear to be no comprehensive collections of the
results of such experiments and investigations. Here,
we report on developing a freely accessible experimental electron backscattering database (https://doi.org/10.
5281/zenodo.7810951). This dataset is the first publicly
available extensive experimental data collection for electron backscattering coefficients from solid targets as a
function of beam energy, angle of incident, and target
thickness.
2
ACQUISITION AND VALIDATION
METHODS
The electron backscattering coefficient can be measured experimentally or calculated theoretically. Many
experimental investigations have been reported in the
literature for the backscattering of electrons from solid
targets; the results of these investigations were found
to show considerable inconsistencies.20–23 One reason
would be that most of the reported experimental results
have been measured under conventional vacuum conditions, with some at different pressure levels. Also, in situ
surface cleaning was considered in few of these investigations, while most of the reported η measurements are
from samples with a thin surface film of contaminants.
Such layers can change the target thickness, altering its
backscattering behavior to another target material.
The theoretical treatment of the fundamental scattering process is complicated. The electron backscattering
coefficient is mainly calculated analytically or statistically using the Monte Carlo simulation. In recent
decades there has been continuous improvement
in Monte Carlo modeling of electron beam interactions with solids as a powerful theoretical tool widely
used to study electron backscattering. CASINO Monte
Carlo simulation software24 and an EGSnrc usercode25 customized for backscatter calculations are the
most frequently used approaches to obtain electron
backscattering. Analytically, some theoretical expressions have been developed based on a single elastic
scatter collision assumption in which the backscatter coefficient depends only on the atomic number
(Z) of the scatterer and is independent of electron
energy; such as Everhart’s single scattering approach,26
Archard’s point source diffusion model,27 and Thiimmel’s continuous-diffusion-depth model.28 However, a
good model describing the backscattering of solids
should include single scattering and diffusion, and
the contributions of double and multiple scattering
processes. Despite many investigations on electron
backscattering, there is some disagreement among the
proposed theories and various viewpoints. Furthermore,
some methods were not significantly predictive of the
experimental results. The papers typically describe certain limiting cases where the results are difficult to
evaluate. On the other hand, some empirical formulas
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
fit the electron backscattering data with linear or polynomial functions of the atomic number (Z), others with
exp(−Z) or log(Z+1) functions. While some theoretical
formulae are energy independent, it was experimentally indicated that backscatter depends on the electron
energy.29–31
Existing theories commonly describe certain limiting
cases or are challenging to evaluate. Also, because
of the essentially random manner in which electrons
lose their energy, current theoretical treatments are
not totally satisfactory. By simulation methods, on the
other hand, numerical results can be obtained, requiring
expensive computer calculations to achieve the acceptance uncertainty. Due to the mentioned limitations of
the theoretical and simulation approaches, experimental measurements are considered as the most reliable
method to obtain backscatter coefficients. A reasonable
amount of experimental data are available for electron
backscattering, representing an extensive range of incident projectile angles and energies, target species, and
experimental geometries. Available measured data are
mainly in the form of research papers written in several
different languages. They are inserted within text documents in a table or graph format, stated in different units,
and with different levels of precision. Joy’s database
of measured electron backscattering as a function of
the atomic number of the target and the incident beam
energy assembled for 45 elements and 13 compounds
of bulk materials was limited to normal incidence and
energies up to 100 keV, primarily focusing on electron
microscopy and microanalysis applications. However,
there appears to be no comprehensive collections of the
results of such experimental investigations. As a result,
anyone requiring specific information has to explore the
literature in the hope of discovering a reported value
that must then be considered reliable. Augmenting Joy’s
database, we established a comprehensive database on
electron backscattering as a function of target atomic
number and thickness, and electron energy and incident
angle. For the period from 1940 to the present, literature
searches were done to find all citable, published references in this field; yet the search cannot be affirmed to
be complete.Table 1A (see Appendix) contains a numerical list of the references used in the database. Unlike
Joy’s database, we included the title of the publication
where available.
Following Joy’s approach, a set of rules were used
for data collection: (a) Only experimental observations
were included. Findings from calculations and fittings, as
well as values that were not explicitly marked as experimental, were excluded. (b) All experimental data were
taken from their original sources. (c) There had been no
attempt to eliminate any results due to their accuracy,
precision, or quality. Our new set of experimental data
were digitized electronically from their original graphs if
they were not available in tabular form. The backscattering coefficients were expressed as a percentage to
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For validation, a limited number of data points were
compared to recently published MC results.32 The
validation set consists of the calculated maximum
backscattering coefficients and experimental observations for Cu under 20, 50, and 100 keV electron beam, as
presented in Figure 1. The numbers next to the symbols
correspond to different references for the experimental observations. The simulation results are denoted as
“MC”, shown as solid black circles in the graph.
3
F I G U R E 1 Maximum backscattering coefficient from bulk Cu at
20, 50, and 100 keV electron source. The references for the
experimental observations are indicated by the numbers next to each
data point. Results of the simulations are shown with black symbols
and denoted as “MC”.
compile a self -consistent database. All energies and
incident angles were expressed in keV and degree units,
respectively. Compared to the Joy’s database, data were
plotted in the format of graphs to provide a visual representation of data that is easier to interpret than raw data.
The information is now presented in a clear and succinct manner,making it simpler for others to comprehend
the data. Graphs also allow for easy comparison across
multiple dataset as well as making informed predictions
about future trends.
DATA FORMAT AND USAGE NOTES
The presented database is available over the World
Wide Web. As a result, the database can be accessed
by users using a browser without the need for any additional software or a subscription. As of this writing, a
total of 3566 records were stored in the database for
50 solid elements and 19 compounds at electron energies ranging from 0.1 keV to 15 MeV. There are three
folders in this web interface for energy, orientation, and
thickness dependencies of the electron backscattering
coefficient, containing 67, 14, and 14 files, respectively.
Figure 2 depicts a portion of the web interface’s folders
and files.
The database was formatted as a collection of ASCII
files for general use. Both the commonly used .csv standard format and the .txt format were used to store the
data. Data for different materials are presented in a
consistent style so that they may easily be compared.
The name of the material and elemental atomic number
is included in each file. The first and second columns
F I G U R E 2 Folders and files in .txt format within our database. The data files in .csv format are also available in three other similar folders
that are part of the Zenodo repository.
24734209, 2023, 9, Downloaded from https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.16604 by University Of Toronto Mississauga, Wiley Online Library on [18/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
TA B L E 1
Description of the files (.txt format) in the database
Folder
File name and contents
Energy
dependence
Ag.txt, Al.txt, Ag.txt, As.txt, Au.txt, B.txt, Ba.txt, Be.txt, Bi.txt, C.txt, Ca.txt, Cd.txt, Co.txt, Cr.txt, Cu.txt, Fe.txt, Ga.txt, Ge.txt,
Hf.txt, Hg.txt, In.txt, Ir.txt, K.txt, La.txt, Mg.txt, Mn.txt, Mo.txt, Nb.txt, Ni.txt, Pb.txt, Pd.txt, Pt.txt, Sb.txt, Sc.txt, Se.txt,
Si.txt, Si-a.txt, Sm.txt, Sn.txt, Sr.txt, Ta.txt, Te.txt, Ti.txt, Tl.txt, U.txt,V.txt, W.txt, Y.txt, Zn.txt, Zr.txt, AlSi.txt, CuAu.txt,
COAT725.txt, ITO.txt, IZO.txt, PETEOS.txt, Plastic.txt, Resist.txt, SiO2.txt, TaC.txt, Ti-6Al-4V.txt, TiC.txt, UO2.txt, U-V
Resist.txt, V2O5.txt, ZrC.txt, Interconnect-line Al.txt (Electron backscattering coefficients as a function of energy of
normal incident electrons for bulk targets)
Energy.xlsx (Collected data and plots of backscattering coefficients versus energy)
Orientation
dependence
Ag.txt, Al.txt, Au.txt, Be.txt, C.txt, Cu.txt, Mo.txt, Ta.txt, Ti.txt, U.txt, Fe.txt, Nb.txt, UO2.txt (Electron backscattering
coefficients as a function of energy and angle of incident for bulk targets)
Orientation.xlsx (Collected data and plots of backscattering coefficients versus beam angle for different energies)
Thickness
dependence
Ag.txt, Al.txt, Au.txt, Bi.txt, Cu.txt, Pb.txt, Ti.txt, U.txt, V.txt, ZnS.txt, PbF2.txt, CuAu.txt, Ti-6Al-4V.txt (Electron
backscattering coefficients as a function of energy and film thickness)
Thickness.xlsx (Collected data and plots of backscattering coefficients versus film thickness for different energies)
were always labeled E, where E denotes the energy values (in keV), and η which is the electron backscattering
coefficient (in %), followed by either electron incident
angle or target thickness. The last column contains the
reference number (see Table 1A in Appendix) for the
data. The names of the targets were used to name
the files. Additionally, an xlsx file in some folders contains the collected data sorted in ascending order of
energy and plotted in graph form for better visualization. The material of interest can be chosen from various
alphabetical sheets.High-level visual summaries,trends,
and patterns in Excel enables the user to analyze data
and better comprehend it. All files in the web-based
user interface can be downloaded. Table 1 represents
a description of the .txt files in the database. Table 2
and Figure 3 depict an example of information supplied
in the three .txt files and the plotted data for Al target,
respectively.
4
DISCUSSIONS
Although electron backscattering coefficients can be
obtained using CASINO, a Monte Carlo code in C language for electron beam interaction, calculations are
limited to bulk targets of fixed thicknesses only. Likewise,
a customized EGSnrc user code has been developed for
backscattering coefficient calculations, but it can only be
used for low-energy regimens. Monte Carlo calculations
are very time-consuming for higher energies and bulk
targets, on the other hand, can only be carried out if sufficient experimental data are available. An open-access
database in physics quantities can be incredibly helpful
for researchers as it provides them with easy access to
a vast amount of data and information. This can save
researchers a lot of time and effort in collecting and
analyzing data, allowing them to focus on their research
and make new discoveries. Additionally, an open-access
database can facilitate collaboration and knowledgesharing among researchers, leading to more efficient
and effective research outcomes.
Collecting the electron backscattering data in this
work revealed that there exists little or no data for most
elements in the periodic table, while results for complex
materials of dosimetric interests are also almost nonexistent, as evident from Table 3. To identify any hidden
patterns and problems in the dataset which may not
be immediately apparent looking at raw data, we displayed the frequency distribution of existing information
by energy and atomic number. As shown in Figure 4, the
most experiments were performed using the low energies and low atomic number targets. It was found that
only 25% of all data were measured at energies above
100 keV which indicates the lack of data for higher
energies of particular importance in radiotherapy applications. Inconsistent experiment results were also found
by means of data visualization supplied in the Zenodo repository. This discrepancy was most noticeable
in the energy dependence of electron backscattering
coefficients. The uncertainty in a measurement arises,
in general, from personal errors, systematic errors, or
random errors. The experimenter might take the measurement erroneously, with poor technique, or with bias
if they expect that the data will support their prediction.
Some inaccuracies can be attributed to faulty design,
inaccurate calibration, or the observer’s prejudice and
observational style. Identifying exact reasons for inconsistent experiments in the reviewed publications was
impossible since the measurements were not always
clearly defined and conditions that could affect the measurements were not carefully specified. All measured
results were reported in this work regardless of wide
disagreements in some measurements. Further investigations are therefore necessary to judge the reliability
and uncertainty of any particular data point.
This database provides a framework for quantitatively
understanding and interpreting electron backscattering,
as is required, for example, in semiconductor device
research, as well as a comprehensive source of experimental data for testing analytical and Monte Carlo
models of electron beam interactions. As noted earlier,
this dataset was initially prepared by Joy for limited bulk
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TA B L E 2 An example of information provided in .txt files for the Al target: (a) Energy dependence, (b) Orientation dependence, and (c)
Thickness dependence. The first and second columns are energy (in keV), and the electron backscattering coefficient (in %), followed by either
electron incident angle or target thickness. The last column contains the reference number for the data, according to Table 1A (see Appendix).
(a)
(b)
(c)
E (keV)
η (%)
Reference
E (keV)
η (%)
Angle
(degree)
0.5
21.5
(1) Cleaned sample
20
16.9
10
1
21.2
20
18.6
20
4000
0.49
0.1
1.5
20.6
20
21.6
30
4000
0.57
0.15
2
20.3
20
26
40
4000
1.18
0.3
2.5
20.1
20
32.4
50
4000
1.97
0.5
3
19.7
20
40.9
60
4000
2.68
0.6
3.5
19.5
20
52.6
70
4000
2.74
0.7
4
19.1
20
59.8
75
4000
2.91
0.85
4.5
18.8
20
68.7
80
4000
3.08
0.95
5
18.4
40
15.6
10
4000
3.1
1
6
18
40
17.4
20
4000
3.1
1.25
1
19.1
40
20.4
30
4000
3.16
1.35
1.5
18.6
40
24.9
40
4000
3.28
1.3
2
17.7
40
31.2
50
4000
3.23
1.67
2.5
17.5
40
39.8
60
4000
3.2
1.85
3
17.4
40
50.9
70
8000
0.52
0.16
3.5
16.9
40
58.4
75
8000
0.68
0.34
4
16.7
40
67
80
8000
0.71
0.68
4.5
16.3
60
15.2
10
8000
0.85
0.88
5
16.3
60
16.9
20
8000
1.21
1.38
0.8
19.8
60
19.8
30
8000
1.33
1.57
1
19.5
60
24.3
40
8000
1.24
2.35
1.2
18.9
60
30.6
50
8000
1.26
2.59
1.4
18.2
60
39.3
60
8000
1.26
2.78
1.6
17.9
60
50.5
70
8000
1.25
3.77
1.8
17.5
60
58
75
8000
1.25
4.35
(1) non-cleaned sample
(2)
targets for energies up to 100 keV. We have expanded
Joy’s database to incorporate all relevant details as well
as data extracted from more recent research that may
be found via reference search engines, such as information on thin films, different incidence angles (if available),
and broader energy spectra (up to 15 MeV). Compared
to the Joy’s database of 1430, the data were compiled into a database of 3566 data points of electron
backscattering coefficients.
While the data by itself can be useful in a myriad of
clinical and industrial applications related to radiation
dose calculations, the cleaned and ordered format of
the data could be seen as even more valuable. It can
assist physicists in creating more robust theories and
identifying more precise relationships between the
various factors affecting electron backscattering. Additionally, in one medical application, data can be utilized
to estimate the amount of off -focal radiation (stray
radiation) produced by backscattering electrons in kilo-
Reference
E (keV)
η (%)
Thickness
(g/cm2 )
Reference
(8)
4000
0.36
0.05
(5)
voltage x-ray tubes. Because electron backscattering
coefficients from anode materials indicate the amount
of off -focal component, researchers can model more
realistic and efficient x-ray systems by reducing the
effect of off -focal radiation on x-ray tube output, image
quality, and patient exposure by knowing these data as
a function of incident electron energy, target thickness,
and atomic number.33 Moreover, electron backscattering
data can be used in designing a multilayer detector
structure consisting of a detector-sensitive volume
and a metal back-reflector layer. Our database can be
utilized to determine the proper material and optimum
thickness of the backscattering layer to achieve signal
enhancement in radiation dosimetry.32 Besides, as the
radiation dose can be calculated using an equation
incorporating the electron backscattering coefficients,
according to the established linear relationship between
the backscattered electron fluence and the deposited
dose in the detector’s active volume,32 our database
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ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
F I G U R E 3 Electron backscattering coefficient for Al target. (a) Energy dependence, (b) Electron beam orientation dependence, and (c–f)
Target thickness dependence. Y-axis in all graphs represents electron backscattering coefficient η(%). Parts (c–f) show film thickness
dependency of the η for a different range of low and high electron energies. The original unit of the thickness was kept.
24734209, 2023, 9, Downloaded from https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.16604 by University Of Toronto Mississauga, Wiley Online Library on [18/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
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TA B L E 3 A list of the target materials included in the references
used to compile our database, organized alphabetically.
Target material
Reference number (see
Table 1A in Appendix)
Silver (Z = 47)
1–18, 35
TA B L E 3
(Continued)
Target material
Reference number (see
Table 1A in Appendix)
Silicon (Z = 14)
6, 10, 12, 14, 15, 17, 18, 24, 25
Si-a (Silicon amorphous)
38
Aluminum (Z = 13)
1–5, 7–23, 35, 36
Silicon Dioxide (SiO2)
29
Al-Si alloy
4
6
Arsenic (Z = 33)
Samarium (Z = 62)
13
Tin (Z = 50)
6, 10, 13, 14, 18
Gold (Z = 74)
1–3, 6–10, 12, 14, 15, 17, 18, 19,
24, 35, 36
Strontium (Z = 38)
18
Boron (Z = 5)
6
Tantalum (Z = 73)
5, 6, 8, 13, 14, 18, 21, 26, 0, 31
Barium (Z = 56)
18
Tantalum Carbide (TaC)
31
Beryllium (Z = 4)
7–11, 13, 15, 18, 25
Bismuth (Z = 83)
6, 10, 13, 14, 17, 35
Carbon (Z = 6)
1, 4, 5, 6, 8, 9, 12–14, 16–18, 21, 26
Calcium (Z = 20)
16, 18
Cadmium (Z = 48)
6, 18
Cobalt (Z = 27)
6, 13, 14
COAT725 (wafer coat)
38
Tellurium (Z = 52)
6, 10, 13, 14, 32
Titanium (Z = 22)
6, 8, 12–14, 17–19, 21
Ti-6Al-4V
19
Titanium Carbide (TiC)
31
Thallium (Z = 81)
18
Uranium (Z = 92)
5, 6, 8–10, 13–15, 21
Uranium dioxide (UO2)
21
U-V Resist
29
Vanadium (Z = 23)
6, 14, 17, 19
33
Chromium (Z = 24)
6, 12, 14, 17
Copper (Z = 29)
1–12, 14, 15, 17–20, 26–28
CuAu (50%Cu-50%Au)
19
Vanadium Pentoxide
(V2O5)
Iron (Z = 26)
6, 8, 12–14, 16, 17, 26
Tungsten (Z = 74)
6, 10, 12–14, 16, 18, 34
Gallium (Z = 31)
18
Yttrium (Z = 39)
18
Germanium (Z = 32)
6, 10, 12, 13, 15, 18
Zinc (Z = 30)
6, 12, 18, 35
Hafnium (Z = 72)
6
6, 14, 17
Mercury (Z = 80)
Zirconium (Z = 40)
18
Zirconium Carbide (ZrC)
31
Indium (Z = 49)
10, 18
Interconnect line Aluminum
38
Iridium (Z = 77)
14
Indium tin oxide (ITO)
29
Indium Zinc Oxide (IZO)
29
Potassium (Z = 19)
1
Lanthanum (Z = 57)
18
Magnesium (Z = 12)
6, 14, 18
Manganese (Z = 25)
14
Molybdenum (Z = 42)
10, 12–14, 16, 18, 21, 26
Niobium (Z = 41)
8, 13
Nickel (Z = 28)
6, 12–14, 16–18, 30, 31
Lead (Z = 82)
18, 20, 35, 37
Lead fluoride (PbF2)
35
Palladium (Z = 46)
14
PETEOS
38
Plastic
25
Platinum (Z = 78)
6, 12, 14, 16, 18, 26, 31
Resist (e-beam –PMMA)
38
Antimony (Z = 51)
6, 10, 14
Scandium (Z = 21)
18
Selenium (Z = 34)
18
(Continues)
can be utilized to test this theory and demonstrate the
accuracy of any suggested dose calculation formula.
The present database also assists in the design of
internal shields that incorporate appropriate materials
to reduce backscattering while minimizing overall shield
thickness for improved clinical setup and simplicity of
utilization. Furthermore, because thin-films are crucial
to modern materials science, microelectronics, semiconductor technology, and biology, and because film
thickness and the electron backscattering coefficient
are correlated, our database provides an essential
tool for determining thin-film thickness and enables
scientists to develop an optimized thin-film design.
Last but not least, this database provides researchers
with knowledge about the backscattering effect on
image quality when developing an imaging system
since backscattering introduces a source of noise to
the detection signal in imaging systems.
The data availability is still very limited for many solids
and almost non-existent for compounds because experimental physicists are motivated to collect data that
are useful to their particular area of study. Machine
learning techniques should be well adapted to produce the missing values for various target materials,
24734209, 2023, 9, Downloaded from https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.16604 by University Of Toronto Mississauga, Wiley Online Library on [18/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
ELECTRON BACKSCATTERING COEFFICIENTS DATABASE
FIGURE 4
Distribution of existing experimental data by energy and atomic number.
including thin films, and expanded ranges of energies.
LiF, one of the most popular thermoluminescent detectors, or CdTe, which is regarded as the next-generation
x-ray detector in medical imaging applications34 are
examples of such missing data. This extensive collection of easily accessible data enables researchers
to develop sophisticated Monte Carlo simulations of
electron-solid interactions and validate their predictions. The literature has demonstrated the benefits of
combining powerful machine-learning techniques with
conventional computational modeling to develop the
required data. Therefore, another substantial application of the presented database is that it could be used
with combination of Monte-Carlo to design the optimal
detector device for a range of energies. These data are
useful in determining the ideal parameters, before running time consuming simulations or pursuing them in
the laboratory which in turn helps to reduce the costs
of building prototypes. Furthermore, recently introduced
physics-based machine learning allows investigators to
analyze the physical principles behind electron- solid
interactions by extracting features and evaluating their
importance.
5
CONCLUSIONS
This paper presents a database on electron backscattering coefficients from different target materials. The
data were stored in compressed files freely available
for all users via the Zenodo repository (https://doi.org/
10.5281/zenodo.7810951). The present database contains a wide range of data on the backscattering of
electrons, including information on the energy and angle
of the incident electrons, as well as the composition
and structure of the target materials. The database
is designed to be used by researchers in a variety
of fields, including medical physics, physics, materials science, and engineering. It can be used to help
researchers understand the fundamental physics of
electron backscattering, as well as to develop new
detectors, materials, and technologies that rely on this
phenomenon.
This is a scientifically valuable open-access resource
for researchers who are interested in electron backscattering, as it provides a wealth of data and information
that can be used to inform and guide research in this
area. It can be freely used by students, universities,
and research laboratories in their research endeavors.
A reference to this paper should be made whenever
the results from using these data are presented or
published.
AC K N OW L E D G M E N T S
I am deeply grateful to all those who played a role in the
success of this database article. The author received no
financial support for the research and publication of this
article.
C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors do not have any conflict of interest.
REFERENCES
1. Goldstein JI, Newbury DE, Michael JR, et al. Scanning electron
microscopy and X-ray microanalysis. Springer; 2017.
2. Verhaegen F, Seuntjens J. Monte Carlo study of electron spectra
and dose from backscattered radiation in the vicinity of media
interfaces for monoenergetic photons of 50–1250 keV. Radiat
Res. 1995;143(3):334-342.
3. Buffa FM, Verhaegen F. Backscatter and dose perturbations for
low-to medium-energy electron point sources at the interface
between materials with different atomic numbers. Radiat Res.
2004;162(6):693-701.
4. Chetty IJ, Curran B, Cygler JE, et al. Report of the AAPM Task
Group No. 105: issues associated with clinical implementation of
Monte Carlo-based photon and electron external beam treatment
planning. Med Phys. 2007;34(12):4818-4853.
5. Kim SH, Pia MG, Basaglia T, et al. Validation test of Geant4
simulation of electron backscattering. IEEE Trans Nucl Sci.
2015;62(2):451-479.
6. Isayev O,Oses C,Toher C,Gossett E,Curtarolo S,Tropsha A.Universal fragment descriptors for predicting properties of inorganic
crystals. Nat Commun. 2017;8(1):15679.
7. Dong Y, Wu C, Zhang C, Liu Y, Cheng J, Lin J. Bandgap
prediction by deep learning in configurationally hybridized
24734209, 2023, 9, Downloaded from https://aapm.onlinelibrary.wiley.com/doi/10.1002/mp.16604 by University Of Toronto Mississauga, Wiley Online Library on [18/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
5928
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
graphene and boron nitride. npj Comput Mater. 2019;5(1):
26.
Meredig B, Antono E, Church C, et al. Can machine learning
identify the next high-temperature superconductor? Examining
extrapolation performance for materials discovery. Mol Syst Des
Eng. 2018;3(5):819-825.
Pilania G, Wang C, Jiang X, Rajasekaran S, Ramprasad R. Accelerating materials property predictions using machine learning.
Sci Rep. 2013;3(1):1-6.
Tawfik SA, Isayev O, Spencer MJS, Winkler DA. Predicting thermal properties of crystals using machine learning. Adv Theory
Simul. 2020;3(2):1900208.
Ward L, Agrawal A, Choudhary A, Wolverton C. A generalpurpose machine learning framework for predicting properties of
inorganic materials. npj Comput Mater. 2016;2(1):1-7.
Yang L, Da B, Ding Z. Ensemble machine learning methods: predicting electron stopping powers from a small experimental database. Phys Chem Chem Phys. 2021;23(10):60626074.
Akbari F, Taghizadeh S, Shvydka D, Sperling NN, Parsai EI.
Predicting electronic stopping powers using stacking ensemble
machine learning method. Nucl Instrum Methods Phys Res, Sect
B. 2023;538:8-16.
Parfitt WA, Jackman RB. Machine learning for the prediction
of stopping powers. Nucl Instrum Methods Phys Res, Sect B.
2020;478:21-33.
Chen Z,Andrejevic N,Drucker NC,et al.Machine learning on neutron and x-ray scattering and spectroscopies. Chem Phys Rev.
2021;2(3):031301.
Isaksson LJ, Pepa M, Zaffaroni M, et al. Machine learning-based
models for prediction of toxicity outcomes in radiotherapy. Front
Oncol. 2020;10:790.
Aldraimli M, Osman S, Grishchuck D, et al. Development
and optimization of a machine-learning prediction model for
acute desquamation after breast radiation therapy in the
multicenter REQUITE cohort. Adv Radiat Oncol. 2022;7(3):
100890.
Ebrahimi S, Lim GJ. A reinforcement learning approach for
finding optimal policy of adaptive radiation therapy considering
uncertain tumor biological response. Artif Intell Med. 2021;121:
102193.
Joy DC. A database on electron-solid interactions. Scanning.
1995;17(5):270-275.
Miller WE. Transmission and backscatter coefficients of 1.0-to
3.0-mev electrons incident on some metals and alloys. National
Aeronautics and Space Administration; 1970:5724.
Neubert G, Rogaschewski S. Backscattering coefficient measurements of 15 to 60 keV electrons for solids at various angles
of incidence. Phys Status Solidi. 1980;61(2):709.
Wright KA,Trump JG.Back-Scattering of megavolt electrons from
thick targets. J Appl Phys. 1962;33(2):687-690.
5929
23. Massoumi G, Lennard WN, Schultz PJ, Walker AB, Jensen
KO. Electron and positron backscattering in the medium-energy
range. Phys Rev B. 1993;47(17):11007.
24. Hovington P, Drouin D, Gauvin R. CASINO: a new Monte
Carlo code in C language for electron beam interaction—Part I:
description of the program. Scanning. 1997;19(1):1-14.
25. Rogers ESMAaDW. Benchmarking EGSnrc in the kilovoltage
energy range against experimental measurements of charged
particle backscatter coefficients. Phys Med Biol. 2008;53:18.
26. Everhart T. Simple theory concerning the reflection of electrons
from solids. J Appl Phys. 1960;31(8):1483-1490.
27. Archard GD. Back scattering of electrons. J Appl Phys.
1961;32(8):6.
28. Niedrig H. Analytical models in electron backscattering. Scan
Electron Microsc. 1982;1982(1):5.
29. Ebert P, Lauzon A, Lent E. Transmission and backscattering of
4.0-to 12.0-MeV electrons. Phys Rev. 1969;183(2):422.
30. Staub P-F. Bulk target backscattering coefficient and energy distribution of 0.5-100 keV electrons: an empirical and synthetic
study. J Phys D: Appl Phys. 1994;27(7):1533.
31. Hussain A, Yang LH, Zou YB, et al. Monte Carlo simulation study
of electron yields from compound semiconductor materials. J
Appl Phys. 2020;128(1):015305.
32. Akbari F, Shvydka D. Electron backscattering for signal
enhancement in a thin-film CdTe radiation detector. Med Phys.
2022;49(10):6654-6665. doi:10.1002/mp.15813
33. Ali E, Rogers D. Quantifying the effect of off -focal radiation on the
output of kilovoltage x-ray systems. Med Phys. 2008;35(9):41494160.
34. Akbari F, Parsai EI, Shvydka D. Large area thin-film CdTe
as the next-generation x-ray detector for medical imaging
applications. High-Z Materials for X-ray Detection: Material Properties and Characterization Techniques. Springer; 2023:23-41.
S U P P O R T I N G I N F O R M AT I O N
Additional supporting information can be found online
in the Supporting Information section at the end of this
article.
How to cite this article: Akbari F. A
comprehensive open-access database of
electron backscattering coefficients for energies
ranging from 0.1 keV to 15 MeV. Med Phys.
2023;50:5920–5929.
https://doi.org/10.1002/mp.16604
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ELECTRON BACKSCATTERING COEFFICIENTS DATABASE