Optimization of Photolithography CD Control Using VWF and Optolith


The progress in semiconductor technology towards even smaller device geometries demands continuous refinements of the photolithography process. Optical projection lithography is still a widely used technology, though it is coming very close to its resolution limit in sub-half -micron regime. Therefore, CD-control and optimization of all stages of photolithography process are the biggest concern of current and future optical lithography.

Traditional method of CD control analyzes the depth-of-focus and exposure latitude using Smile (Bossung) curves and Exposure-Defocuse (ED) Tree. This method is not sufficient because it fails to involve other critical process parameters such as reticle CD, Numerical Aperture,NA, resist thickness, and ABC development parameters into consideration. Moreover, it is very difficult to use the traditional method to control other important metrics (e.g. sidewall angle) simultaneously with CD.

The only feasible approach is to

  • use design of experiment (DOE) for several input variables
  • perform a number of computer simulations and/or lab experiments and measurements
  • build response surface models (RSM) for selected response factors (e.g. measured CD, sidewall angle, final resist thickness)
  • use simulated RSMs for multi-parametrical control of one or several response factors

Moreover, automatic fitting of simulated RSMs to experimental ones is the only reliable way to calibrate the empirical parameters involved in simulation. All these can be done using Optolith and the Automation and Production Tools of Virtual Wafer Fab (VWF).

To demonstrate this approach, a simple DOE was prepared which involves only two input parameters; image defocus and expose dose. All other parameters were constant: reticle CD was 0.5 microns, NA=0.52, resist thickness was 1 micron.

Latin Hypercube random design with only 50 samples was used. It appeared that even these few experimental points were enough to build an acceptable RSM.

Figure 1 shows the RSM presented as a contour plot of measured CD. The contours in upper part of the plot correspond to smaller CDs (overexposed resist), while contours in the lower part correspond to larger CDs (underexposed resist). Only area in the center of the plot (exposed doses = 160 - 180 mJ/cm2, and image defocus between approximately -0.7 and 0.6 microns) corresponds to a measured CD close to reticle CD. This type of plot can be used for estimation of a "window" of defocus and exposure dose values which result in measured CDs within certain tolerances.

Figure 1. ED tree from VWF for a mask feature of 0.5µm.

Another way to analyze the RSM is to build a Smile plot (Figure 2). This is measured CD as a function of defocus for several values of exposure dose. From this plot one can estimate that the best depth of focus can be achieved with exposure dose around = 160 - 180 mJ/cm2. However, it should be also realized that measured CDs will be slightly smaller ( ~0.45 microns) than nominal.

Figure 2. Simple plot from VWF showing optimum exposure dose.

Even this two-parameter RSM analysis has some advantages over traditional CD control method because it needs fewer number of simulations and provides more flexible method of visualization.

In the second DOE two more parameters, reticle CD and NA, were added. Around 300 simulation points were enough to build acceptable response surfaces for measured CD and sidewall angle.

The new RSM allows Smile and ED-tree plots for various reticle CDs and NAs to be plotted. It also allows CD control and optimization simultaneously for several line widths. For example, Figure 3a , Figure 3b and Figure 3c show how depth of focus changes with the exposure dose for 3 values of reticle CD. It is obvious that the optimal dose for one CD is not the optimum for another. This type of analysis may help to find an optimal solution because different lines in the layout could appear in different focal planes. Therefore depth of focus may be not so critical for some linewidths but could be very crucial for others.



Figure 3. Depth of focus curves for 3 reticle CDs and 3 exposure doses.


The next series of plots (Figure 4a, Figure 4b and Figure 4c) shows how drastically depth of focus curves depend on numerical aperture. It means that NA could serve as a very sensitive optimization parameter. Finally, Figure 5 demonstrates sidewall angles vs Focal Position.



Figure 4. Depth of focus curves for 3 reticle CDs and 3 numerical aperatures.

Figure 5. Averaged sidewall angles vs
defocus for different exposure doses.

It has been shown that the combination of Optolith and VWF can serve as a powerful tool for advanced CD control and optimization of modern photolithography processes.