A Design-of-Experiments Approach
Figure 3: Plots of line width vs. pitch. The lines are a guide to the eye. The 10 trend lines correspond to the ten rows of the experiment as defined in Table 1. The line width appears to be sensitive to the pitch at the low end. Experiment #2 consistently gives the smallest line width.
confidence, so the inclusion of more factors into the model should be considered. We will touch on these fit issues in the discussion below. Finally, the multiple response prediction gives us a 99-percent confidence level that the significant constant C = 16 ± 3 nm, 3 s. Figure 4 contains factor analysis plots that can display
trends and interactions. Plots 4a and 4d show the trends of the given parameters, and the Plots 4b and 4c indicate interactions between them. From Plot 4c we see that the impact of dwell time on line width is the same for all step sizes. Tus, no interaction is indicated. However, Plot 4c shows markedly different behavior at the smallest dwell time, revealing that an
Figure 5: Plot of gap width as function of pitch for experiment 2. The 48-nm pitch result is not included in order to emphasize the trend at small pitch. The solid line is a best fit to a straight line, and the equation of that line is displayed as well.
interaction or nonlinearity exists that has not been accounted for. In Figure 5, we see the trend for the gap width. It should be expected that the gap will shrink in direct proportion to the pitch, but the linear fit of the data (if we concentrate on just the smaller pitches) shows that in fact the gap only shrinks about half as fast as pitch.
Discussion Tese results are encouraging. Te line and gap widths are
the smallest that the authors are aware of for deposition on a bulk surface. Te values of the constant term C in the DOE indicate that lines 13–17 nm can be expected and that complementary gap widths 6–10 nm can be comfortably achieved. Te process is very stable, and the greatest challenge perhaps is to accu- rately measure the features because they are so small. Results of similar magnitude have been observed when carrying out the deposition of insulating lines or when doing fine etching. Tese will be reported at a later time when thorough investigations are completed. Tree items remain present
outstanding in the
Figure 4: DOE factor analysis plots for the 48-nm pitch pairs. The factors and interaction testing in each matrix element is indicated along the top and left of the matrix of plots (Step Size and Dwell Time). Based on the curves in (a) and (d), it is ascertained that smaller step size and longer dwell time give narrower lines. The family of curves in (b) do not have a uniform trend, indicating that some dependencies probably have not been accounted for. See discussion in the main text.
2011 May •
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analysis, which should be considered when we look at the low R2 values obtained; this fit measure became even lower as the pitch of the line pairs was reduced below the 48-nm example shown. Such a poor fit in the analysis indicates that other factors, not captured by the model, are influencing the results. One item is the impact of dwell time on line width, for varying step size, as seen in Figure 4. It sheds some
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