Modeling of Block Copolymer Self-Assembly

The directed self-assembly of block copolymers using nanolithographically-defined templates is showing great progress in fabricating arbitrary patterned media for device and mask fabrication at length scales on the order of tens of nanometers. The current approach in manufacturing these patterns involves firstly defining a template by a top-down lithography process such as electron beam or photolithography and then casting and annealing the block copolymer films on these templates for the bottom-up self-assembly to take place. The resulting morphologies are then observed and characterized through various microscopy techniques. For simple periodic patterns where the template directing the self-assembly is used to increase long range order and increase throughput, designing the necessary template for a desired pattern is straight forward by changing template feature placement position and symmetry. However, for arbitrary patterns that are needed in patterning more complex integrated circuit layout patterns, designing a minimal template to get the desired structure is not as straight forward. By using self-consistent field theory (SCFT) simulations combined with a template minimization scheme, an inverse design solution to this problem is possible. In these simulations, the optimal position of template features are found for a given target morphology through a random walk energy minimization process. These post positions then represent the necessary and sufficient conditions needed to produce the target morphology. Additionally, forward SCFT simulations are used in predicting the thin film morphologies for a given input template as well as verifying the solutions of the inverse simulations. These traditional SCFT simulations have given insight into the 3D structures of block copolymers of varying film thickness confined by posts of varying height, diameter, and spacing as shown. Phase diagrams of these various input parameters are then used to predict and compare with the morphologies observed in experiments. In all of these simulations, the ultimate goal is to be able to design block copolymer patterns with minimal experimentation.