New model of polymer silylation: Application to lithography

Abstract

A new model of polymer silylation is proposed. This model takes into account the reaction of the silylating agent with the hydroxyl groups of the polymer and the relaxation rate of the polymer after reaction. The diffusion coefficient of the silylating agent is supposed to be a function of the expansion of the polymer matrix. At the interface between the silylating agent and the polymer, it is assumed that sorption driven by the pressure of the silylating agent, and desorption driven by the concentration of the silylating agent can occur. The resulting differential equations are solved using a finite element technique and the influence of the main parameters, namely, the reaction rate, the relaxation rate, and the diffusion coefficients is studied.

Stress dependent silylation model and two-dimensional profile simulation

“…6 Reaction-diffusion models proposed by Jaghold et al 7 and Pierrat 8 include gas phase incorporation and diffusion of the silylating agent into the film. The proposed model takes into account three relevant mechanisms: ͑a͒ the relaxation of the polymer during silylation, ͑b͒ the resultant increase in the diffusivity of the silylating agent as a function of the resist matrix expansion, 8 as well as ͑c͒ a local reaction rate retardation due to stresses associated with nonuniform resist swelling. 9 In this article, we describe a new mechanism-based model of polymer silylation that will be used to explain the influence of the silylation process parameters on the silicon profiles in the resist.…”

A Fully Coupled Computational Model of the Silylation Process

“…Equation (21) is sixnilarto expressions given in [15] and [19]; for w = O Equations (21) and (22) are expressionsof Fick's law (where for lack of data we have assumed e@al diffusion coefficientsfor .4 and B).…”

“…Pierrat [15]proposed the exponential dependence of the diffuion coefficient on the expanded, silylated resist concentration c~, arguing that the filon coefficient should be larger in the silylated areas due to the swellingand decreasesin density and glass transitiontemperatureof the polymer that occur in the silylation process. Note that Crank [271assumed an exponential dependence of the diffurion coefficient on penetrant concentration to describe non-Fickian dif?usionin polymers.…”

“…Pierrat [15]. His model accounted for the reaction of the silylating agent with the resist polymer and the relaxation rate of the polymer after reaction.…”

“…The silylation reaction (1) assumesthat one molecule of the silylating agent A reacts with one repeat unit of the unexposed and uncrosslinkedpolymer C to form one molecule of product species 13 and one repeat unit of silylated, unexpanded polymer D. The relaxationreaction (2) impliesthere is a time scale associated with swellingof the silylated polymer ( [15], [19]). The mass production rates of the species are given by:…”