ISSN 1027-4510, Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques, 2017, Vol. 11, No. 4, pp. 853–864. © Pleiades Publishing, Ltd., 2017.
Original Russian Text © Yu.A. Novikov, 2017, published in Poverkhnost’, 2017, No. 8, pp. 73–86.
Monte Carlo Method in Scanning Electron Microscopy.
1. Modeling and Experiment
Yu. A. Novikov
Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409 Russia
Received November 1, 2016
Abstract—Results of modeling by the Monte Carlo method of signals from a scanning electron microscope
examining rectangular grooves in silicon are compared with experimental results obtained for a scanning elec-
tron microscope operating in the secondary slow electron collection mode. The comparison is performed for
the peaks of signals characterizing the primary electron beam near the walls of rectangular grooves: the widths
and amplitudes of the peaks, the integral contributions of the peaks, and the positions of the peaks relative to
the walls of the grooves. The parameters and their dependences on the primary electron energy are compared.
All dependences are very different in terms of the parameters of the peaks and their dependence on the pri-
mary electron energy. This proves that the traditional representation of the Monte Carlo method does not
work in scanning electron microscopy.
Keywords: Monte Carlo method, statistical modeling, scanning electron microscope, virtual scanning elec-
tron microscope, secondary slow electrons, image-formation mechanisms
Scanning electron microscopy is widely used in
various areas of science, engineering, and technology
[1‒4]. However, the widest application of scanning
electron microscopy has been attained in microelec-
tronics and nanoelectronics [4‒6]. In [7, 8], it was
shown that measuring the linear sizes of elements of
microchips is an important stage of microchip tech-
nology, substantially reducing the costs of developing
the technology and producing microchips.
For this purpose, in Russia, a system for a scanning
electron microscope (SEM) was developed, which
converts the sizes from the Primary length standard
(meter) to the nanoscale and makes it possible to mea-
sure the linear sizes of elements of microchips up to
10 nm [9, 10].
To date, a method for measuring the linear sizes of
microchip elements up to 30 nm with a SEM has been
developed . In order to justify the measurement of
such small sizes and theoretically develop new meth-
ods for measurements, a virtual scanning electron
microscope (VSEM) was created [12‒16]. Virtual
measuring devices, to which the VSEM belongs, can
be created by two methods: imitation of the operation
of a real device  or by the simulation of information
obtained on a real device .
For a VSEM, the operation of a real SEM is imi-
tated by statistical modeling known as the Monte
Carlo method. This method was developed in the
middle of the 20th century and has gained wide appli-
cation due to the simplicity of implementation and the
advent of high-performance personal computers. For
more than half a century, an uncountable number of
works concerning the Monte Carlo method have been
published, including works describing its application
to scanning electron microscopy. These works are rep-
resented most completely in review . Here, we add
some works [19‒25] published both before and after
this review and lacking in  for different reasons.
In , it was shown that a VSEM cannot be cre-
ated by the Monte Carlo method (in [14‒16], it was
created on the basis of a simulator). However, the
application of the Monte Carlo method to scanning
electron microscopy continues to widen (see, e.g.,
It should be noted that, for the first time, the dis-
agreement of the results of modeling by the Monte
Carlo method  with the results of experiments with
a SEM was demonstrated in . However, this work
was published a long time ago in a journal that is hard
to come by in Russian. In this context, it is necessary
to consider in detail the possibilities of application of
the Monte Carlo method to scanning electron micros-
copy, the advantages and drawbacks of the method,
and modeling results and to compare these results with