ISO 21466:2019

INTERNATIONAL ISO
STANDARD 21466
First edition
2019-12
Microbeam analysis — Scanning
electron microscopy — Method for
evaluating critical dimensions by CD-
SEM
Analyse par microfaisceaux — Méthode d’évaluation des dimensions
critiques par CD-SEM
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 8
5 Generation of Model-based Library (MBL) . 8
5.1 Basic components of a MBL simulator . 8
5.1.1 Electron probe model . 8
5.1.2 SE signal generation model .10
5.1.3 SE signal detection model .11
5.2 Model of specimen .12
5.2.1 Specimen structure and parameters .12
5.2.2 Specimen specification .15
5.2.3 Generation methods of specimen geometry .15
5.3 Monte Carlo simulation .15
5.3.1 Input parameters .15
5.3.2 Beam-specimen interaction .16
5.4 MBL file structure .16
5.4.1 Variable type and value .16
5.4.2 Model description file .20
5.4.3 Parameter specification file .21
5.4.4 Preparation of library data.21
5.4.5 MBL data structure .22
5.4.6 MBL data file format .22
6 Acquisition of a CD-SEM image.23
6.1 Acceptable image .23
6.2 Specimen tilt .23
6.3 Image quality .23
6.4 Selection of the field of view .23
6.5 CD-SEM image data file .23
7 CD determination .23
7.1 Determination of pixel size.24
7.2 Selection of the field of interest .24
7.3 Coordination and normalization .24
7.4 Matching procedure.25
7.4.1 Interpolation .25
7.4.2 Convolution .25
7.4.3 Matching .26
7.4.4 Averaging .30
8 Module functions and relationship .31
9 Uncertainty of CD measurement .33
Annex A (normative) Flow charts of procedures .35
Annex B (informative) Example of model description file .39
Annex C (informative) Example of parameter specification file .40
Annex D (informative) Example of CD evaluation .41
Bibliography .44
Foreword
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This document was prepared by Technical Committee ISO/TC 202, Microbeam analysis, Subcommittee
SC 4, Scanning electron microscopy (SEM).
Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv © ISO 2019 – All rights reserved

Introduction
Nanostructures need strict dimensional control to meet the demands of the semiconductor industry.
Critical dimension (CD) is the minimum size of a feature on an integrated circuit that impacts the
electrical properties of the device, whose value represents the level of complexity of manufacturing.
At nanometer scale, measurement uncertainty control becomes more difficult with much smaller
dimensions. A determination method with algorithm for accurate measurement is a key for CD
valuation. CD-SEMs (critical dimension scanning electron microscopes) are one of the main tools for
CD measurement in semiconductor manufacturing processes, where secondary electrons (SEs) are
the signal source for CD-SEM imaging of surface structure. The CD-SEM image displays the structure
geometry, but the image contrast is not a perfect representation of the structure morphology. The
detected intensity linescan profile of SE signals carries the information about the sample shape and
composition, beam size and shape and the information volume generated by the electron beam-solid
interaction. Restricted by the physical mechanism in the processes of SE signal generation and emission,
the SE signal profiles show an edge effect which leads to difficulty for accurate CD value determination
with image contrast. A reliable CD determination method which bases on physical principle of SE signal
emission is necessary.
Many factors, for example the specimen chemical composition, structural geometric parameters, beam
conditions and other specimen/instrument factors (charging, vibration and drift), can affect CD-SEM
image contrast and hence the CD measurement result. Topographic contrast in the SE mode is resulted
from the enhanced SE emission from an edge as well as tilted local surface in relative to the incident
beam. The quantitative description of contrast or SE intensity profile is crucial in CD metrology.
The physical mechanisms that dominate quantitative measurements by CD-SEM have been well
understood. The CD determination algorithm is based on physical modelling of SE generation and
emission and gives adequate consideration of the influence of various experimental factors during
electron beam-specimen interaction. This document employs the model-based library (MBL) method
for accurate CD determination by CD-SEM. MBL is superior to simpler, unsophisticated, arbitrary
methods that disregard the physics of signal generation, and report only a meagre number, potentially
with unacceptably high bias. MBL uses the whole waveform of the signal, so it can provide results
with less bias and better size and shape accuracy. Once the library is set up, there is essentially no
time penalty for using MBL. Construction of MBL is done with a Monte Carlo (MC) simulator which is
considered as an excellent approach to take into account of every possible physical factor that may affect
signal intensity and shape of linescan profiles. The library generation can be sped up tremendously by
suitable multicore computing environment and MC software that is optimized for a specific measurand.
Such obtained MBL relates the measured signal linescan profiles to both specimen parameters and
instrumental parameters. The library database is consisted of the simulated SE linescan profiles,
having a one-to-one correspondence to a specified value of parameter set. By matching the shape of SE
linescan profile taking from a measured CD-SEM image with those simulated beforehand and stored in
a MBL database, the best fitted CD values used in MC modelling are selected.
INTERNATIONAL STANDARD ISO 21466:2019(E)
Microbeam analysis — Scanning electron microscopy —
Method for evaluating critical dimensions by CD-SEM
1 Scope
This document specifies the structure model with related parameters, file format and fitting procedure
for characterizing critical dimension (CD) values for wafer and photomask by imaging with a critical
dimension scanning electron microscope (CD-SEM) by the model-based library (MBL) method. The
method is applicable to linewidth determination for specimen, such as, gate on wafer, photomask, single
isolated or dense line feature pattern down to size of 10 nm.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
critical dimension
CD
minimum geometrical feature size limited by the photolithography technology used for the
fabrication process
3.2
CD metrology
measurement of the width of line and space for a trapezoidal line structure model
Note 1 to entry: Extended CD metrology includes the measurement of top CD, middle CD, bottom CD, height,
sidewall angle, top rounding and foot rounding. Figure 1 shows schematically the definition of CDs.
Note 2 to entry: The term “top rounding” indicates a circular arc at the top corner, which is tangent to the top
surface and side surface of a trapezoidal line, and whose value is represented by the circular radius.
Note 3 to entry: The term “foot rounding” indicates a circular arc at the bottom corner, which is tangent to the
bottom surface and side surface of a trapezoidal line, and whose value is represented by the circular radius.
Note 4 to entry: More frequently CD represents the size of a feature on an integrated circuit or transistor that
impacts the electrical properties of the device.
Note 5 to entry: Top rounding and foot rounding are not designed parameters.
3.3
critical-dimension scanning electron microscope
CD-SEM
special instrument for measuring CDs (3.1) of the fine patterns formed on a semiconductor wafer
by producing magnified images (3.4) of a specimen (3.19) by scanning its surface with a focused
electron beam
Note 1 to entry: It is mainly used in the manufacturing lines of electronic devices of semiconductors and
optimized for dimensional metrology task, and differs from a general-purpose laboratory SEM in several
aspects: 1. primary electron beam irradiates the sample at normal or nearly normal incidence condition; 2. the
measurement repeatability around 1 % 3σ of the measurement width is guaranteed by improving magnification
calibration to the maximum extent; 3. fine pattern measurements on the wafer are automated.
Figure 1 — Definition of CDs: top CD, middle CD, bottom CD, height, sidewall angle, top rounding
and foot rounding
3.4
image
two-dimensional representation of the specimen (3.19) surface generated by SEM
Note 1 to entry: A photograph of a specimen taken using an SEM is a good example of an image.
[SOURCE: ISO 16700:2016, 3.2]
3.5
SEM imaging
action of forming an image (3.4) by a mapping operation that collects electron signals emitted from the
specimen (3.19) surface and passes the digital signal intensity information into the storage devices
3.6
SE image
scanning (3.9) of electron beam images (3.4) in which the signal is derived from a detector that
selectively measures secondary electrons (3.20) (electrons having energies less than 50 eV) and is not
directly sensitive to backscattered electrons
Note 1 to entry: Intensity of digital CD-SEM image is adjusted to 8 bit (or other) depth of grayscale and does not
equal to the detected physical number of secondary electron signals.
2 © ISO 2019 – All rights reserved

[SOURCE: ISO 23833:2013, 4.4.11, modified — Note 1 to entry added.]
3.7
electron probe
electron beam focused by the electron optical system onto the specimen (3.19)
[SOURCE: ISO 22493:2014, 7.1]
3.8
electron probe size
beam size
beam width
diameter of a circle that contains 50 % of the total electron probe (3.7) current
Note 1 to entry: For an ideal Gaussian probe shape in the radial direction:
 
1 r

Gr|eσ =−xp (1)
()
 
b
 
2 2
22πσ σ
 
bb
the electron probe size is determined by the standard deviation (σ ) as d =22ln2σ , which is equal to the full
b
pb
width at half maximum (FWHM) of the Gaussian peak.
3.9
scanning
action of obtaining time-controlled movement of the electron probe (3.7) on the specimen (3.19) surface
3.10
linescan profile
signal intensity as function of coordinate along a straight line across an image (3.4)
3.11
focusing
aiming the electrons onto a particular point using an electron lens
[SOURCE: ISO 22493:2014, 3.1.4]
3.12
convergence angle
half-angle of the cone of the beam electrons converging onto the specimen (3.19)
[SOURCE: ISO 22493:2014, 7.1.1]
3.13
working distance
distance between the lower surface of the pole piece of the objective lens and the specimen (3.19) surface
Note 1 to entry: In the past, this distance was defined as the distance between the principal plane of the objective
lens and the plane containing the specimen surface.
[SOURCE: ISO 22493:2014, 4.5.2]
3.14
charging effect
distortion of signal intensity in SEM imaging (3.5) of non-conductive specimens (3.19) due to
accumulation of spatial charges in homogeneously distributed and hence the establishment of surface
electric potential, which alters primary electron incidence (including landing energy and position) and
all emitted electron signal properties
Note 1 to entry: The effect is a time dependent phenomenon and mainly related to current density and beam energy.
3.15
pixel
smallest discrete image (3.4) data element that constitutes an SEM image
[SOURCE: ISO 22493:2014, 5.2.4]
3.16
pixel size
length of the pixel (3.15), measured at a specimen (3.19) surface
Note 1 to entry: For a square or circular pixel, the horizontal and vertical pixel sizes should be the same.
[SOURCE: ISO 22493:2014, 5.2.5]
3.17
contrast
difference in signal intensities between two arbitrarily chosen points of interest in the image (3.4) field
3.18
graphics file format
archival digital format for storing the contents of the frame store
Note 1 to entry: The most popular image file formats are: bitmap (BMP), graphics interchange format (GIF), tagged
image format (TIF) and joint photographic experts group (JPG). The TIF format can preserve all data and keeps
the size of each pixel in its header. Consequently, this format is preferred to maintain the integrity of the images.
[SOURCE: ISO 22493:2014, 5.6.4, modified — “TIF format is the scientific format that preserves” is
changed to “TIF format can preserve”, admitted term "image file format" removed.]
3.19
specimen
sampled material designated to be examined or analysed
[SOURCE: ISO 22493:2014, 4.5]
3.20
secondary electron
SE
electron emitted from the specimen (3.19) by the excitation of loosely bound valence electrons of the
specimen in electron inelastic scattering (3.31) events and in a cascade production process as a result of
bombardment by excitation beams, e.g. electrons, ions and photons
Note 1 to entry: By convention, an emitted electron with energy lower than 50 eV is considered as a secondary
electron when primary energy is above 50 eV.
3.21
SE yield
total number of secondary electrons (3.20) per incident electron
[SOURCE: ISO 22493:2014, 3.4.1]
3.22
SE angular distribution
distribution of secondary electrons (3.20) as a function of their emitting angles relative to the
surface normal
[SOURCE: ISO 22493:2014, 3.4.2]
3.23
SE energy distribution
distribution of secondary electrons (3.20) as a function of their emitting energies above the vacuum level
[SOURCE: ISO 22493:2014, 3.4.3, modified — added “above the vacuum level”]
4 © ISO 2019 – All rights reserved

3.24
SE tilt dependence
effect on secondary electrons (3.20) of the specimen (3.19) tilt which accompanies a change in incident
beam angle
[SOURCE: ISO 22493:2014, 3.4.5]
3.25
Monte Carlo simulation
MC simulation
broad class of computational algorithms that uses statistical sampling techniques to obtain numerical
results of a math model (Eckhardt 1987)
Note 1 to entry: The calculation models stochastic physical processes in the electron beam-specimen interaction
and SEM image formation (Shimizu 1992; Joy 1995). The incident electron beam strikes the surface of the
specimen, then a series of elastic and inelastic scattering (3.31) process takes place inside the specimen for the
incident electrons and generated SEs. Connection of the spatial location of scattering event forms an electron
trajectory. Tracking of electron trajectory is terminated when an electron is absorbed by losing its kinetic energy
to below surface barrier (3.39) or leave from the specimen surface. Calculation includes the determination of free
path as a function of energy, the outcome of a scattering event, i.e. the new direction, position and energy of a
primary electron and a SE if it is generated.
Note 2 to entry: The simulation for electron beam-specimen interaction is made of the following process (Ding
1996). A primary electron enters into the specimen at an angle α of incidence, which may not be normal to the
local surface even for a normal incident beam onto the substrate plane, shall suffer a scattering after flying
over a distance of free path. This electron step length obeys an exponential probability distribution where the
mean free path is determined by the sum of inverse electron total elastic scattering cross section and electron
inelastic mean free path. By MC simulation technique a particular value of variable shall be randomly sampled
from a given probability density distribution for a continuous variable or from a probability for a discrete
variable with a random number uniformly distributed in the interval of 0-1. In discrete scattering model the
property of scattering event being either elastic or inelastic is determined by another random number based on
the proportion of elastic scattering or inelastic scattering in the total cross section. If it is elastic the scattering
angle is sampled from the differential elastic scattering cross section by a random number. If it is inelastic,
the associated energy loss and scattering angle are sampled from the corresponding differential or double-
differential inelastic scattering cross sections. The new moving direction after scattering can then be determined
to derive the updated coordinates of electron after passing by a new step length (Figure 2). Accompanied with
electron energy loss in an inelastic event, one SE will be generated and its information on the energy, position
and direction will be stored in a stack so that they could be read out after finishing tracing of an incident electron
trajectory. All the simulated electrons, either primary or secondary, shall generate further cascade SEs along
their trajectories in the solid target. If the energy of an electron reaching the surface is high enough to overcome
the surface barrier it is then emitted from the local surface.
Note 3 to entry: MC simulation of SE image and SE linescan profile is performed by counting number of emitted
SEs by calculating a certain number of primary electron trajectories, which are incident onto a location at
specimen surface corresponding to an image pixel, and the generated cascade SE trajectories inside the specimen
for a primary beam scanning the specimen surface.
Key
E electron kinetic energy
S sampled electron flight length
ΔE sampled electron energy loss in an inelastic scattering event
θ sampled electron scattering angle (polar angle) in an elastic or inelastic scattering event
φ sampled electron azimuthal angle in an elastic or inelastic scattering event
Figure 2 — Schematic diagram of Monte Carlo simulation of electron trajectory
3.26
model-based library
MBL
database of calculated SE linescan profiles (3.10) with a MC simulation method based on physical
modelling of electron beam interaction with a specimen (3.19) in the CD-SEM (3.3) imaging process,
having one-to-one correspondence between the simulated SE linescan profile and a parameter set for
geometric modelling of specimen topography and beam condition
3.27
MBL simulator
specific MC simulation model and simulation software for producing a MBL database
3.28
scattering cross section
total scattering cross section
effective area that quantifies the essential likelihood of a scattering event when an incident beam strikes
a target object, mathematical description of the probability of a scattering event (elastic or inelastic)
Note 1 to entry: Scattering cross-section is usually measured in units of area.
3.29
differential scattering cross section
cross section which is specified as a function of some final-state variable, such as particle angle and/
or energy
6 © ISO 2019 – All rights reserved

3.30
elastic scattering
deflection of an electron in the Coulomb potential of an atomic nucleus where electron energy transfer
is negligible and large-angle deflection is possible because electron mass is much smaller than the mass
of the nucleus
Note 1 to entry: Note to entry 1: This type of electron collision is mainly responsible for the electron diffusion in
a solid.
3.31
inelastic scattering
energy loss event of an electron due to its interaction with solid electrons, which resulting in an
excitation of electronic state, and accompanied with small angle of deflection.
Note 1 to entry: Note to entry 1: This type of electron collision is responsible for slowing down of incident
electrons and the production of SEs.
3.32
inelastic mean free path
average distance travelled by an electron through a medium before losing energy, mathematical
description of the probability of an inelastic scattering event
Note 1 to entry: Inelastic mean free path is usually measured in units of length.
3.33
optical constants
refractive index n(ω) and extinction coefficient k(ω), as functions of photon energy ω
3.34
dielectric function
dielectric data
complex function which describes the electrical and optical properties of a material versus wavevector
q and photon energy ω
Note 1 to entry: Dielectric function ε(ω) = ε + iε relates to refractive index n(ω) and extinction coefficient k(ω)
1 2
2 2
through ε = n − k and ε = 2nk.
1 2
3.35
energy loss function
physical quantity describing electron energy loss probability or the differential inelastic scattering
cross section (3.28), which is given via dielectric function (3.34) by Im{}−1 εω()q,
3.36
optical energy loss function
energy loss function (3.35) at long wavelength limit, Im −10εω,
{}()
3.37
plasmon
quantum of collective electron oscillations in a metal or a semiconductor
3.38
phonon
quantum of lattice vibrations in a solid
3.39
surface barrier
potential barrier that an electron to overcome for emission from a solid into vacuum, being the electron
affinity for semiconductors and insulators or the sum of Fermi energy and work function for metals
Note 1 to entry: Surface barrier is usually given in unit of eV.
4 Symbols and abbreviated terms
CD critical dimension
MBL model-based library
MC Monte Carlo
SE secondary electron
SEM scanning electron microscope/scanning electron microscopy
5 Generation of Model-based Library (MBL)
A MBL is produced by a comprehensive MC simulation with a MBL simulator for a given combination set
of experimental parameters and specimen geometric parameters, which are predetermined by a MBL
database developer. MBL is a set of simulated SE linescan profiles with one-to-one correspondence to a
specific set of instrument- and sample-related parameters.
NOTE A MBL database developer represents an individual and/or an organization who produces a MBL
database by using a MBL simulator in accordance with Clause 5.
5.1 Basic components of a MBL simulator
A complete MBL simulator is made of several components for CD-SEM image simulation (References [7]
[20][55][19][63]) by including electron probe model, SE signal generation model and SE signal detection
model, which are then denoted as the descriptor of the MBL simulator. The values of the descriptor are
noted in the MBL description document file, Model.txt.
5.1.1 Electron probe model
The electron probe intensity profile (i.e. beam shape and probe diameter) influences the CD-SEM
image sharpness and hence the linescan profile. The probe diameter is broadened by the aberrations
[50][51]
of the objective lens, which is an important instrumental parameter of MBL . Electron intensity
distribution within the beam is never ideal in practical cases. One approximation is a Gaussian shape
with a constant size (spot size), another one is an “hourglass shape” beam with or without asymmetrical
above- and under-focus form. Any of these can be non-perpendicular to the sample. Accounting for a
couple of degrees of “stray” tilt can further improve the accuracy of MBL.
a) Gaussian beam model
[10]
The geometric theory of electron-probe formation assumes Gaussian profile of the probe shape
[11]
, and the distribution in the lateral direction is given by Formula (2):
 
1 x
Gx|eσ =−xp (2)
()  
b
 2 
2πσ 2σ
 
b b
An ideal electron beam assumes the landing spot size on the surface of specimen is zero. By this
modelling, specimen geometry is independent of probe size for a MBL data simulation. To minimize
the library size, it is recommended to simulate SE linescan profiles only for an ideal electron beam
in MBL construction; the Gaussian distributions for different probe sizes can be later used in a
convolution procedure to derive linescan profiles corresponding to finite probe sizes in MBL curve
[13]
matching .
b) Focusing beam model
This model considers an electron beam having a convergence whose angle is defined by the
[53][62]
angular aperture . At the focal plane electrons are distributed in a certain shape of profile not
necessarily follows the exact Gaussian function, having an effective beam width in each of the x- and
8 © ISO 2019 – All rights reserved

y-directions. Electrons are more divergently distributed horizontally when arriving on surface if it
is away from the focal plane. By this model, the mean direction of the incident electrons is normal
to the substrate plane but incident directions of individual electrons may deviate from the mean
incident direction. The density distribution of electrons arriving at specimen surface is influenced
by the distance away from the focus plane. Therefore, there is no exact definition of electron probe
size for landing electrons as it relates to specimen topography. This makes differences on SE
emission intensity for incident electrons striking on different locations of a topographic surface,
[43][44]
e.g. between the top of the line, the sidewall, and the substrate .
The simulation of SE linescan profiles should be carried out for each value set of focusing parameters
(Figure 3), i.e. the nominal probe size or effective beam width d (nm) which is given on the focal plane,
p
convergence angle α (mrad), working distance d (mm), and defocus value d (nm) as the distance
s f
between the focal plane and the top surface. The focusing position is measured from the specimen top
surface where it is defined as the just-focus position (i.e. d = 0), while d < 0 and d > 0 correspond to
f f f
under-focus and over-focus cases, respectively, where the vertical coordinate is positive along the beam
incidence direction. An incident electron trajectory with its incident direction and landing position
are determined by random sampling two horizontal positions in aperture plane and focal plane from
[62]
Gaussian distributions and connecting them as a straight ray towards the landing surface . At the
aperture plane and focal plane, the beam widths are given respectively by d tanα and d . The obtained
s p
MBL curves are directly matched with the measured one without convolution.
NOTE Focusing beam model excels Gaussian beam model in accuracy of description of SE linescan profiles
by adding further three parameters but enlarging greatly the MBL data file size. d =22ln2σ when α =0.
p b
Key
H height of a trapezoid line
α convergence angle of incident electron beam
d working distance
s
d the distance between the focal plane and the top surface
f
d the effective beam width or the diameter of least confusion disc along the beam axis
p
Figure 3 — Schematic diagram of focusing electron probe shape at different landing positions of
a line structure
5.1.2 SE signal generation model
Primary electrons hitting the specimen surface will diffuse in a specimen through a series of elastic and
inelastic scattering processes. The excitation and emission of SEs are the result of these fundamental
scattering processes inside the solid specimen. The MC simulation of SEM imaging process is based
on a physical model of such electron-solid interaction under various approximations (References [25]
[15] [29] [31] [26] [33] [11]). A reasonable physical model of SE signal generation process is essential
to a MBL simulator and database construction. The physical model includes the following interaction
processes.
a) Elastic scattering
The screened Rutherford cross section was employed in an early MC simulation model of elastic
scattering. However, as the spin-orbit coupling becomes increasingly important in the low-voltage
region below 1 kV and for heavier elements, which is not taken into account in the Rutherford
model, the Mott cross section should be used. Results based on the Mott theory are found in better
agreement with the available experimental data for low energy electrons. The differential elastic
[34]
scattering cross section in the Mott theory can be obtained numerically by a partial wave
[39][24]
expansion method and by solving the relativistic Dirac equation in a central field . As Mott
cross section is not represented by a specific analytic expression, the calculated numerical values
of the differential cross section are stored in a table in a MC program for simulation.
b) Inelastic scattering
There are several different inelastic interaction mechanisms on the fundamental physics of electron
inelastic scattering that relates to the SE generation including inner-shell excitation, single electron
excitation and plasmon excitation. Among them bulk plasmon is a collective longitudinal oscillation
of the electron gas, whose decay can also excite SEs. The unified treatment of these inelastic
channels is through the use of dielectric function ε(q,ω), where q is momentum transfer and ω
is energy loss. The differential inverse inelastic mean free path is proportional to the energy loss
function, Im −1 εωq, . The energy loss and the associated SE generation in individual scattering
{}()
[14][33]
events can be treated by MC random sampling .
0 4
The abundant dielectric data for ε(0,ω) or optical constants in the loss energy range of 10 − 10 eV
[35][21]
experimentally measured are available and compiled . The advantage to use them is that the
electronic excitation in real materials is more accurately described. They are used as the input data
to a MC simulation. There are multiple algorithms to extrapolate the optical energy loss function
Im −10εω, into the (q,ω)-plane, for example, single pole approximation (SPA), full Penn
{}()
[36]
algorithm (FPA) and Howie’s finite sum by using the plasmon-pole form of Lindhard dielectric
[41]
function . The dielectric functional model influences largely the calculated SE energy distribution
and absolute SE yield, but may less on the SE linescan profile which is a relative intensity.
Another model of electron inelastic scattering is based on the use of Bethe’s stopping power
[31][49]
equation under the continuous slowing-down approximation . The electron energy loss is
evaluated through the multiplication of stopping power and step length between two successive
elastic scattering events. As Bethe’s stopping power equation is invalid in the low energy region, the
[25]
Joy’s modified equation with an empirical extension to low energy region is useful. In addition,
for free-electron-like materials the plasmon excitation is well-defined and a discrete inelastic
[5][6]
scattering model is available .
Dielectric functional formalisms (FPA and SPA) are better than the stopping power equation
approach under the continuous slowing-down approximation and the discrete scattering channel
approach is the more accurate description of electron inelastic scattering and secondary electron
signal generation for a wide range of materials; and FPA is superior to SPA.
c) SE generation
According to individual inelastic scattering model (FPA and SPA), the energy loss is transferred
to a knock-on electron and to cause a SE generation. The moving direction of the generated SE is
assumed to be isotropic. After its birth, the SE will suffer similar elastic and inelastic scattering as
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primary electrons and cause cascade production of low energy SEs. Only those emitted electrons
[14]
into vacuum with their kinetic energies lower than 50 eV are counted as true SE signals .
Individual inelastic scattering models (FPA and SPA) combined with cascade production model can
[15][16]
provide reasonable absolute SE yields in agree with experimental data range .
In the stopping power equation approach in continuous slowing-down approximation the amount
of SE signals for one trajectory within one step length are estimated via energy loss. This approach
can only give relative yield-energy dependence and the absolute SE yield determination needs a
fitting of multiplication factor by comparing the calculation with experiments.
d) SE emission
When an electron is reaching the surface from interior of a specimen for emission, the refraction
of electrons by the surface barrier at the local surface needs to be considered because the surface
barrier influences the energy and angular distribution of slow electrons. Two approaches exist
for transmission function. The classical one as a step function only requires the kinetic energy
[14][27]
is higher than the surface barrier, while the quantum mechanical representation gives the
varied emission probability depending on the kinetic energy as well as the ejection angle.
NOTE In the case of charging the surface barrier changes as surface electric potential.
e) Phonon scattering
The interaction between an electron and lattice is a process of phonon scattering. The energy of
electron changes slightly but the momentum has a significant change; especially at low energies,
electrons have high probability to interact with the lattice vibration. This inelastic scattering
channel is particularly not negligible for an insulator.
f) Charging of insulating specimen
Charge accumulation with electron beam irradiation can distinctly change electric potential on
[12]
specimen surface and cause image distortion . The time variation of electrostatic field between
the specimen and detector influences SE trajectories and hence signal intensity. The charging effect
evidently affects SE image contrast for insulators and therefore has a potential risk of improper CD
evaluation. An implementation of charging effect simulation by a MC method needs to include the
[40][28]
following aspects .
The charge production, diffusion and deposition in the specimen: negative charges (SEs) and
positive charges (holes) are produced in electron inelastic scattering events. They are determined
by tracking incoming probe electrons and outgoing SEs and BSEs. Th
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