3.2.1 Focus Effects and Process Window

The effect of focus on a projection lithography system is a critical part in understanding and controlling a lithographic process. The depth of focus and the process window derived from it are two important metrics for practical characterization. Simulation proves an invaluable tool for predicting focus effects, generating process windows, and determining realistic values for the depth of focus.

In Section 2.1 the importance of the depth of focus DOF was theoretically discussed with the help of (2.2). However, in practical applications the definition of the DOF is more involved since a change in focus not only alters the final resist profile but also increases the sensitivity to other processing errors, whereby the dependence on exposure dose is of primary concern. Resist profiles are often described by three parameters related to a trapezoidal approximation of the profile: the linewidth or critical dimension (CD), the sidewall angle, and the final resist thickness. Since the effect of focus depends on exposure, the only way to judge the response of the process is to simultaneously vary both focus and exposure. The focus-exposure matrix obtained this way can easily be visualized by a Bossung plot [48]. Figure 3.2 shows two examples using first linewidth and then exposure as the response.

  

Figure 3.2: Bossung plots are used to visualize the focus-exposure matrix. The response can either be energy or any other characteristic parameter, with linewidth as the most important one.

The two other profile parameters of sidewall angle and resist loss can be plotted in the same graph with the linewidth. The result is a process window, i.e., the region of focus and exposure that keeps the final resist profile within prescribed specifications. An example is given in Figure 3.3.

  

Figure 3.3: The process window is determined by plotting all three geometrical resist parameters of linewidth, resist loss, and sidewall angle in the same Bossung plot. A simple graphical analysis provides exposure latitude versus depth of focus curves for either random or systematic errors.

The process window describes the process capability that must match the process requirements to guarantee an acceptable yield. A simple graphical analysis of the process window is based on fitting all ``maximum'' rectangles or ellipses inside the shaded area representing systematic and random errors respectively. Plotting their height versus their width, i.e., exposure latitude versus depth of focus, provides the most concise representation of the coupled effects of focus and exposure on the lithography process (cf. Figure 3.3).