Principal Investigator Karl Berggren
Directed self-assembly of block copolymers can generate complex and well-ordered nanoscale patterns for lithography. Previously, self-consistent field theory has been commonly used to model and predict the block co-polymer morphology resulting from a given template. In this work, we map block copolymer self-assembly onto an Ising model using two-dimensional post lattice template. We describe a simple and fast Ising-model-based simulation method for block copolymer self-assembly. With the Ising lattice setup, we demonstrate Ising-model-based logic gates.
To define the Ising lattice, we used a post lattice template with horizontal and vertical pitch equal to the equilibrium block copolymer periodicity, L0. After block copolymer processing, we defined a binary state, +1 or −1, between each adjacent pair of posts. We assigned +1 to a state when two adjacent posts were connected by a block copolymer structure, and −1 otherwise. The Ising Hamiltonian is given by where J’s and h’s were assumed to be independent of lat- tice location. We calculated the minimum Hamiltonian configuration using simulated annealing and compared the simulation results with previously reported results.
To perform Ising-model-based computation, we encoded Boolean operations into the ground states of Ising lattices by designing specific Hamiltonians. We can also show a template design for a buffer where a boundary was defined by incommensurate double posts. Inside the boundary, an input state and an output state were defined. Prior to block copolymer processing, the input state was determined by the orientation of double posts while the output state was undetermined. After block self-assembly, the output state was set equal to the input state, performing the buffer operation.