synopsisThe scattering of light by a two-dimensional spherulite of radius R is calculated when there is disorder of optic axis orientation with respect to the radius. Special cases are considered when (1) the disorder occurs in the radial direction only, ( 2 ) the disorder occurs in the angular direction only, (3) there is combined radial and angular disorder, and (4) the optic axis makes a constant angle with the radius but there is disorder in the twist angle about the axis. I n all of these calculations, a correlation function for disorder is defined and the scattering pattern depends on the ratio of the associated correlation distance to the size of the spherulite. With decreasing correlation distance, the azimuthal dependence of the scattering becomes less and there is a change in the variation of scattered intensity with scattering angles in a manner dependent upon the type of disorder. A more specific model for the random contribution is presented in this paper. In a perfect spherulite it is assumed that all of the crystals are oriented with the axes making a definite angle with respect to the spherulite radii. We shall assume that there is a disorder in crystal orientation within the spherulites and calculate the consequences of such disorder on the scattering .

The effect of birefringence of a polymer film upon its photographic light‐scattering pattern is considered for the case of a single, anisotropic, two‐dimensional spherulite imbedded in a birefringent matrix. It is shown that for the case of a polarizer and analyzer crossed at +45° and −45° to the analyzer, the scattering pattern is modified in a manner agreeing with experimental observation.

Data on tensile strength and elongation at break for a series of Viton A‐HV vulcanizates are discussed. The data were obtained at various extension rates at temperatures from −5 to 230°C (25 ≲ T — Tg ≲ 260°C) on seven vulcanizates having crosslink densities ve (estimated from C1 in the Mooney‐Rivlin equation) from 0.46 × 10−5 to 24.4 × 10−5 mole/cm3. At an extension rate of 1 min−1, an increase in ve affects the tensile strength σb (based on the undeformed cross‐sectional area) and the true tensile strength σbσb (based on the cross‐sectional area of a deformed specimen) as follows: σb is essentially constant at a low temperature; it passes through a decided maximum at intermediate temperatures; and it increases to a plateau at elevated temperatures. In contrast, λbσb decreases markedly at all temperatures, an exception being the most lightly crosslinked vulcanizate(s). Application of time—temperature superposition to the ultimate‐property data gave log aT; its temperature dependence is that typical of nonpolar rubbery polymers. Data on the vulcanizates were compared in corresponding temperature states by plotting log 273σb/T, log 273λbσb/T, and (λb — 1)/(λb — 1)max against logtb/(tb)max, where tb is the temperature‐reduced time to break and (tb)max is the value at which the ultimate extension ratio λb attains its maximum, (λb)max. Except for the most lightly crosslink vulcanizate, the comparison shows that 273λbσb/T and (λb — 1)/(λb — 1)max are substantially independent of (or only weakly dependent on) crosslink density, that 273λb/T increases with ve, and that 273λb/T ∝︁ ve0.6 and λb ∝︁ ve−0.4 at a large value of tb/(tb)max.

A quantitative theoretical calculation is made of the effect of birefringence of the surrounding medium on the light‐scattering pattern from a two‐dimensional anisotropic spherulite. The calculated modification of the light‐scattering pattern is in accord with the prediction previously made on the basis of qualitative considerations and model experiments.

Sub-resolution assist features (SRAF) have been shown to provide significant process window enhancement and across chip line-width variation reduction when used in conjunction with modified illumination lithography. Work previously presented at this conference has focused on the optimization of sraf design rules that specify the predominantly one dimensional placement and width of assist features as a function of layout pitch. This paper will recount the optimization of SRAF style options that specify how SRAF are to behave in realistic two dimensional circuit layouts. Based on the work done to strike the correct balance between sraf manufacturability, CAD turnaround time, and lithographic benefit in IBM's early product implementation exercises, the evolution of sraf style options is presented. Using simulation as well as exposure data, this paper explores the effect of various two dimensional sraf layout solutions and demonstrates the use of model based verification in the optimization of sraf style options.