Mathematical analysis of soft baking in photolithography

The soft baking step of a photolithography process is analyzed theoretically, taking the effect of the temperature dependence of the diffusivity of solvent into account. A coordinates-transform technique is chosen to solve the moving boundary problem under consideration. The temporal variation of the thickness of a film is predicted, and the result obtained justified by fitting experimental data reported in the literature for both poly(methylmethacrylate) film and Shipley UVIII photoresist. We show that, depending upon the types of photoresist film and the operating conditions, the transport of solvent may be controlled by the diffusion of solvent in a film or the convective transport of solvent from the gas–film interface to the bulk gas phase.