Analysis of Experimental Data for Metallic Impurity Out-Diffusion from Deep-UV Photoresist

In a previous study [J. Electrochem. Soc., 146, 3455 (1999)], the radioactive tracer technique was employed to determine the percentages of manganese and zinc impurities diffused from a deep UV photoresist to various underlying substrates at different baking temperatures. For the same baking time, it was found that such "diffusion ratios" do not increase monotonically with temperature. Instead, as the baking temperature increases, the diffusion ratios may first increase and then decrease, first decrease and then increase, or simply decrease monotonically, depending upon the specific impurity/substrate combination. Here, to explain the various temperature dependences of the impurity diffusion ratios, we propose a theory that supplements the Fick's diffusion law with the Arrhenius law, which relates the diffusivities and interfacial segregation coefficients of the metallic impurities to the baking temperature. The theory also makes it possible to extract the values of important physicochemical parameters from raw experimental data, and the methodology is demonstrated in the paper by attempting to analyze the aforementioned experimental data.