Fundamentals of Spin Coating

In 1958, Emslie et al. described the hydrodynamics of a Newtonian and nonvolatile fluid thinning on a rotating disk [28]. By equating the centrifugal forces, creating the outflow, and the viscous drag, responsible for the resistance of the 

Relative final thickness (a.u.) obtained by varying the rotation speed and by keeping all other parameters identical 

Because evaporation has been neglected before this point, one assumes that the viscosity, the density, and the concentration are the same as those of the initial solution. The critical thickness (h ) can then be expressed as a function of the evaporation rate and of the speed. Finally, the final thickness (hf) is equal to the product of h and the volume fraction of nonvolatile species in the initial solution (co). 

The calculation of hf requires knowing the evaporation rate e. However, because this value is extremely difficult to assess due to the feet that it evolves with many parameters (e.g., solution composition, deposition conditions, vapor pressure modification with spinning time, external humidity, and air convection associated with the equipment), one usually prefers to assess the global constant K experimentally, which then permits a rather good prediction of the final thickness with respect to w for a given system solution/spin coater. 

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