Reflow modeling for elongated contact hole shape

Resist reflow is a simple and cost effective technique by which the resist is baked above the glass transition temperature (Tg) after the typical contact hole pattern has been exposed, baked and developed. Resist reflow method can obtain very high resolution without the loss of process margin than any other resolution enhancement techniques that can make the same linewidth. But it is difficult to predict the results of the thermal flow and the process optimization. If the results of reflow process can be exactly predicted, we can save great time and cost. In order to optimize the layout design and process parameters, we develop the resist flow model which can predict the resist reflow tendency as a function of the contact hole size, initial shape and reflow temperature for the normal and elongated contact hole. The basic fluid equation is used to express the flow of resist and the variation of viscosity and density as a function of reflow temperature and time are considered. Moreover surface tension and gravity effects are also considered. In order to build a basic algorism, we assume that the fluid is incompressible, irrotational and Newtonian. First, we consider the boundary movement of side wall and we think the basic equations for free surface flow of fluid as 2-dimensional time-dependent Navier-Stokes equations with the mass conservation equation. Surface tension acting on the interface pressure difference and gravity force that enable the resist flow are also included.