For see-through masks the image structure is quite different from that of the previously analyzed opaque masks (NBS Spec. Publs. 40029, pp. 50-52, and 400-36, pp. 42-44) [32], although the optical system parameters have remained the same. The change which must be made in the mathematical model of the system is in the complex amplitude transmittance function t(x). For chromium-on-glass photomasks, which have a transmittance of a few percent or less, the complex amplitude transmittance was taken as real and the phase retardation of the material ignored. However, for see-through masks, there is an optical path difference between light transmitted

Image profiles and associated parameters were computed for several cases of interest [35]. Figure 24 illustrates the computed image profiles for an objective numerical aperture of 0.90 and varying condenser aperture for the background transmittances and phases indicated. In the course of generating these image profiles, Kintner introduced a new, faster computation method based upon a Fourierseries expansion of the object and computation of the transmission cross-coefficient which characterizes the combined condenser and objective system [36, 37]. This method, which is discussed in connection with darkfield imaging (see sec. 6.3.), is outlined in Appendix C. It enables a reduction in computer time of up to an order of magnitude in some cases along with a slight improvement in accuracy with phase included in the complex amplitude transmittance of the object.

Because the transmittance threshold, T

c' which corresponds to the edge location (denoted by the dashed lines in fig. 24) varies with the amount of phase present as well as the background transmittance of the photomask material, a new expression must be derived for the proper transmittance threshold to be used to establish the edges of the line being measured. As in the case of nearly opaque masks (NBS Spec. Publ. 400-36, pp. 42-44) [32], when a symmetrical impulse response is centered at the edge between two materials, as shown in figure 25, in coherent illumination the threshold at the edge is the ratio of the transmittance computed at this position with respect to the transmittance of the clear area. With a phase change present, T becomes, in coherent limit,

C

e iø

Figure 25.

Schematic illustration showing method of computing threshold at edge with phase shift present.

Table 7 Line-Width Errors Resulting from Locating the Edges at the Center of the Adjacent Dark Band

Objective N.A.

To

Another major goal of the photomask metrology task is the extension of the capability for measuring line widths in the 1- to 10-μm region to include measurements in reflected light. Early in the effort it was recognized that measurements made in reflected light are more difficult to characterize than those made in transmitted light on black-chromium photomasks. Several factors contribute to these difficulties. The reflectance of the materials is much lower than the transmittance resulting in lower signal-to-noise ratio in the photomultiplier output of the scanning photometric microscope. The differences in reflectances are also lower, thereby producing lower contrast imagery. Therefore, the optical-path differences between light reflected from the various parts of the test specimen become important in determining edge locations. The study of transmittance measurements of see-through photomasks (see sec. 6.2.) indicates that the edge image profiles change drastically along with the threshold

Evaluation of Bright-Field and Dark-Field Reflected-Light Systems - One of the two illumination systems, bright field or dark field, is generally used for viewing objects in reflected light with a microscope. The bright-field system, illustrated schematically in figure 26a, uses a beam-splitter to direct the illumination onto the objective which, in turn, focuses the illuminating aperture onto the object. When unfolded, this system corresponds to a transmitted-light system with matched numerical apertures for condenser and objective. Such a system is partially coherent and sensitive to phase (optical-path) differences in the object. Since there is no analytic expression to relate edge location to transmittance threshold, this system is a poor choice for linewidth measurements of the desired accuracy.

In the dark-field system, shown schematically in figure 26b, the illuminating condenser aperture is annular, with an inner radius corresponding to, or greater than, the numerical aperture of the objective. The outer radius is usually as large as practicable in order to gain the maximum flux at the detector. This system, when unfolded, may be analyzed using the theory of partial coherence as was done in the case of transmitted-light systems [32]. However, because the thin, annular condenser aperture has a numerical aper ture greater than that of the objective, a two-dimensional analysis must be made. The computation method used in earlier calculations is prohibitively time-consuming for two dimensional computations, but fortunately the new method of computation introduced by Kintner [36,37], discussed below, reduces the computation time by nearly an order of magnitude; this reduction makes accurate anal ysis of dark-field imagery feasible.

where is the geometrical coordinate in the pupil plane divided by the numerical aperture of the objective lens, w is the full width of the scanning slit in dimensionless coordinates (actual width multiplied by the numerical aperture of the objective lens and divided by the wavelength of the light), and () is the image spatial frequency spectrum in the pupil plane. It should be noted that a non-periodic object may be expressed in terms of a periodic model if a large period is chosen so that the object is effectively isolated and does not interfere with its neighbors. The model and the derivation of

eq (11) are outlined in Appendix C.

(E. C. Kintnert)

Comparison of Calculated and Experimental Dark-Field Image Profiles Line images were calculated from eq (11) for comparison with image profiles experimentally measured with dark-field illumination. One of the difficulties in comparing theoretical and experimentally measured image profiles is determination of the radii of the annular condenser illuminator. For the available transmittedlight, dark-field systems, the numerical apertures of the annuli were available in the literature. However, for reflected-light systems with a reflecting annular illuminator built into the objective, the radii of the annuli could only be estimated from the physical dimensions.