Fundamentals of topographic substrate leveling

Abstract

The leveling of 100–500-μm-wide, 1-μm-deep isolated holes and trenches on a silicon substrate by 1–3-μm-thick silicone oil films was observed by measuring film thickness changes at the centers of the features using a noncontact, interferometric technique. The dependence of the leveling time t on feature width w, film viscosity η, and the initial film thickness h0 was investigated and compared to theoretical predictions. Experimental data were obtained for various values of w, η, and h0. Except when the film thickness was about 1 μm, the data for each different type of geometry fell on a single curve when the degree of leveling or planarization was plotted against T≡tγh30/ηw4 where γ is the surface tension of the film. At the same value of T, the degree of planarization of isolated holes was about twice that of isolated trenches. The planarization versus T curves should apply to all Newtonian liquids and may be used to predict the degree of planarization that will be achieved at specified leveling times by materials having specified values of η, h0, and γ. Thus, the curves may be useful in selecting planarizing materials for semiconductor fabrication steps that require substrate topography leveling. Simulations of the leveling process based on capillarity-driven flow were performed and agreed well with the experimental data. The simulations predicted some interesting and unexpected behavior that was observed experimentally. At short times the planarization became worse before improving at longer times and bumps appeared in the film profiles that apparently were a first step in minimizing surface energy. Such simulations may prove to be useful in predicting the difficulty of planarizing various types of topographic geometries and in designing ‘‘dummy topography’’ that will make them easier to planarize.

Relaxation and intermediate asymptotics of a rectangular trench in a viscous film

“…where η is the viscosity of the film [39][40][41]. The ratio γ/η provides the typical speed of leveling and is termed the capillary velocity.…”

“…The timescale of the longest relaxation time of PS (31.8 kg/mol) at 140 • C is orders of magnitude shorter than the time scales considered here [38], thus we can treat the film as a simple Newtonian liquid. The theoretical description of the problem is thus based on the Stokes equation for highly viscous flows, and the lubrication approximation which states that all vertical length scales are small compared to horizontal ones [39][40][41][42]. A no-slip boundary condition at the liquid-substrate interface and the no-stress boundary condition at the liquid-air interface result in the familiar Poiseuille flow along the z axis.…”

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

“…One method of modifying the film curvature is through gradients in capillary pressure induced by topographical features added to the substrate. [37][38][39] Noninertial coating flows over isothermal substrates with topographical features exhibit similar capillary ridges to the locally heated films but are stable to perturbations due to the restoring flow generated by the capillary pressure gradient induced by the features. 40,41 It was shown from boundary integral solutions of the unsimplified equations of Stokes flow 42 that the film closely follows the topography for capillary numbers ͑Ca͒ that are O͑1͒ or larger but a pronounced capillary ridge develops near the feature for smaller Ca.…”

High precision dynamic multi-interface profilometry with optical coherence tomography

“…where γ is the surface tension, η is the viscosity of the varnish, x is lateral position, h is the varnish thickness, C is concentration, E is the change in thickness as a result of evaporation and ∆t is the time interval [22,23] The simplest parameter to describe roughness is the rms surface roughness. However, this does not contain important spatial information about the surface.…”

“…Multiinterface OCT profiometry is used in this paper to measure dynamic evolution of the surface profile and the cross-correlation between the surface and substrate profiles for two very different drying varnish coatings. The dynamic development of the surface profile is modeled numerically using the differential lubrication approximation to the Navier-Stokes equation [22,23]. The modeled and experimental surface profiles are compared directly to better understand the relationship between the material properties of a varnish and the formation of the surface roughness of varnish on a rough paint-like substrate..…”