А.А. Гурченков, Л.А. Муравей, А.М. Романенков
16
Modelling and optimization of the technology
process by ion beam etching
© A.A. Gurchenkov
1
, L.A. Muravey
2
, A.M. Romanenkov
2
1 Bauman Moscow State Technical University, Moscow, 105005, Russia
2 MATI — Russian State Technological University n.a. K.E. Tsiolkovsky,
Moscow, 103767, Russia
The study tested the problem of optimal control of ion beam etching to minimize geomet-
ric dimensions of the etched elements. This problem is solved by changing the angle of
incidence of the ion beam in relation to the target (IBE method). Advanced techniques for
creating embossing functional layers, including various ways of dry etching, are neces-
sary for making chips with submicron elements. One of those ways is the ion-beam etch-
ing (IBE) based on the action of mono electric ion beams. It permits to change the angle
of the target in relation to the ion beam, thereby to control the angle of the etched ele-
ments. One of the advantages of IBE is the availability of sufficiently accurate mathemat-
ical model. Evolution of the freeform surface during ion beam etching is described by the
essentially nonlinear hyperbolic equation of the first order. The paper describes the func-
tion that determines the angle formed by the beam of the incidence of the ions to the sput-
tered surface, for two-dimensional and three-dimensional cases. To characterize the de-
gree of drifting geometrical dimensions, we introduced the functional and set the problem
of optimal control with non-fixed time. However, due to the special features of the IBE
process, we succeeded in bringing the time-fixed problem to the fixed-time one. For this
problem, using the technique of singular variations, we established Pontryagin maximum
principle. Based on this principle, we designed software package to search for the opti-
mal regimes for different initial profiles. It should be noted, that to search for the optimal
control, it is not necessary to solve the adjoint system, which greatly facilitates the com-
putational process. We also examined the IBE process for the semicircular initial mask.
For comparison, we performed calculations with the optimal control and without it and
made appropriate conclusions.
Keywords:
IBE methods, optimal control, L.S. Pontryagin principle maximum.
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