Stochastic cellular automaton

Algorithm

Materials science

Reversible cellular automaton

Polymer

Automaton

Physics

Mathematics

Cellular automaton

Astronomy

Copolymer

Mobile automaton

Polystyrene

Automata theory

Geometry

Composite material

Combinatorics

Quantum cellular automaton

Block cellular automaton

The formulation of a cellular automaton (CA) model for self-organization processes in low-temperature annealing of a block copolymer in the method of directed self-assembly lithography (DSA) is presented. The model is considered for the geometry of the cylinder and block copolymer AB, A= polystyrene, B= poly(methylmethacrylate). The characteristic cell size of the CA was the length of the Kuhn segment is equal to 1.67 nm, and the quantum of time was taken as 5.3⋅10<sup>−8</sup> s. The CA lattice was a hexagonal prism in the wafer plane, the layers of which are displaced relative to each other in vertical direction. The neighborhood has Neumann template. Mode of CA operation was pair-asynchronous. The cell state was characterized by a set of triples: the polymer number, the number of segments, the segment type (A/B), i.e. the polymers are distributed among the CA cells by their segments. The transition function was correlated with the movement of one segment, and determined by the configuration rule that limits the possible transitions, and selected in a probabilistic way. The random variable draw took into account the state of the extended neighborhood, and the probability values were selected, based on convenience, by a formula similar to the expression of Fermi-Dirac statistics.

Cellular automata method for directed self-assembly modeling