An Analytical Model to Describe the Efficiency of an Immersion Rinsing Process

In this paper, a simple model is presented, describing an immersion rinsing process for flat solid substrates (e.g., semiconductor wafers). It is assumed that together with the solid a layer of processing liquid is transferred into a tank filled with rinsing liquid. The model calculates the replacement of the processing liquid with rinsing liquid as a function of the rinse time and the position in the tank. For static rinsing systems an analytical expression is readily obtained. For dynamic systems (where liquid convection plays a role) the concept of a convective boundary layer is introduced. It is assumed that within this boundary layer diffusion is the dominant transport mechanism while outside the boundary layer convection is dominant. Under these assumptions an analytical expression can also be obtained for dynamic rinsing with the thickness of the convective boundary layer as a process parameter. The resulting analytical expressions can be readily used to calculate the concentration of remaining processing liquid in the vicinity of the solid substrate as a function of rinse time. This provides a good way to determine the efficiency of the rinsing process. Moreover, these expressions allow us to assess the effect of changes in boundary layer thickness and thus can help with the optimization of existing rinsing processes.