The percolation model of resist dissolution

The idea of novolac as an amphiphilic polymer into which the developer penetrates through a chain of hydrophilic sites has led to a mathematical treatment of resist dissolution as a percolative diffusion process. The basic ideas of the percolation theory of dissolution include the following six key facts, (i) The dissolution rate is determined by transport of ions through the percolation zone. 

Percolation theory predicts for the dissolution rate R an equation of the form 

corresponding to the maximum density of free hydroxyl groups in the 

Dammel, Diazonaphthoquinone based Resists, p. 58, SPIE Press, Bellingham, WA (1993). 206t E Yeh, H.Y. Shi, and A. Reiser, A percolation view of novolak dissolution and inhibition, Proc. SPIE 1672, 204 (1992) Percolation view of novolak dissolution and dissolution inhibition, Macromolecules 25, 5345 5352 (1992). 

According to percolation theory, a branch of mathematics dealing with phenomena such as the for mation of connected channels (otherwise called Percolating clusters ) from randomly distributed sites on a grid, such a system would be expected to have a strongly nonlinear response if the number of sites per volume (otherwise called degree of space filling ) is close to a threshold value called the percolation threshold. For more details, see, for example, D. Staufer, Introduction to Percolation Theory, Taylor Francis, London (1985). 

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