A mathematical model for slip phenomenon in a cavity-filling process of nanoimprint lithography

Squeeze flow theory has been used as an effective tool to clarify how and which process conditions determine cavity-filling behavior in nanoimprint lithography (NIL). Conventional squeeze flow models used in NIL research fields have assumed no-slip conditions at the solid-to-liquid boundaries, that is, at the stamp-to-polymer or polymer-to-substrate boundaries. The no-slip assumptions are often violated, however, in micrometer- to nanometer-scale fluid flow. It is therefore necessary to adopt slip or partial slip boundary conditions. In this paper, an analytical mathematical model for the cavity-filling process of NIL that takes into account slip or partial slip boundary conditions is derived using squeeze flow theory. Velocity profiles, pressure distributions, imprinting forces, and evolutions of residual thickness can be predicted using this analytical model. This paper also aims to elucidate how far the slip phenomenon is able to promote the process rate.