ISSN 10637397, Russian Microelectronics, 2014, Vol. 43, No. 4, pp. 277–283. © Pleiades Publishing, Ltd., 2014.
Original Russian Text © A.S. Rudyi, A.N. Kulikov, D.A. Kulikov, A.V. Metlitskaya, 2014, published in Mikroelektronika, 2014, Vol. 43, No. 4, pp. 282–288.
This article is the continuation of studies [1–4].
The authors of  proposed and the authors of 
took into account one deterministic model of surface
erosion under the effect of an ion beam. Currently,
another model of this production process is known.
This is the Bradley–Harper (BH) model , which is
based on the nonlinear differential equation with par
tial parabolic derivatives. It is sometimes called the
Bradley–Harper equation, but it is often reduced to
the better known equation of mathematical physics—
the Kuramoto–Sivashinsky equation.
Both models, the BH model and the nonlocal ero
sion model (NEM) are based on the same theory pro
posed by Sigmund (see, e.g., ) and therefore have
no distinction in principle, but the NEM implies cer
tain refinements and, as shown in this study, can pro
pose a more complex dynamics of solutions. In partic
ular, this is the possibility of appearance of highmode
wave solutions with a sufficiently small wavelength.
The formation of wave nanorelief (WNR) on the
surface of solids is referred to as the most interesting
and least studied phenomena. The wave relief is
formed on the surface of conductors, semiconductors,
and dielectrics with their irradiation by the flows of
both inert and chemically active gases. In this study, we
will first speak about the investigation of WNR forma
tion in a spatial nonlocal model.
Similarly to [1–4], we will consider the equation
which can be written in the simplest variant in the fol
is the surface diffusivity,
is the free path length
of the primary ion, is the angle between the guide of
the ion flow and the normal to the unperturbed surface
before the beginning of the production process, and
the angle between the flow direction and the normal to
that surface, which formed as a result of perturbations at
the micron level (see the BH model). Locally
but it is not obligatory that
= 0. Finally,
is the density of the target material,
density of the flow of primary ions, and
is the sputtering coefficient. If we use the Yamamura
Θ−Θ Θ β Θ
=+γβ − −
sin cos cos
cos( ) 1
γ= β=β− β= Θ Θ
() exp ,
HighMode Wave Reliefs in a Spatially Nonlocal Erosion Model
A. S. Rudyi, A. N. Kulikov, D. A. Kulikov, and A. V. Metlitskaya
Yaroslavl State University N.A. Demidov, ul. Sovetskaya 14, Yaroslavl, 150000 Russia
Received September 20, 2013