Width

To analyze the width of features you have numerous choices which measure the height difference between two dominant features that occur at distinct heights. Width was primarily designed for automatically comparing feature widths at two similar sample sites (e.g., when analyzing etch depths on large numbers of identical silicon wafers).

The Width command is designed to automatically measure width between features distinguished by height, such as trenches and raised features.

The Width command is best applied when comparing similar features on similar sites. Width measurement on dissimilar sites is better performed using the Section command.

Width Theory

The Width algorithm utilizes many of the same functions found in Depth analysis by accumulating height data within a specified area, applying a Gaussian low-pass filter to the data (to remove noise), then rapidly obtaining height comparisons between two dominant features. For example, [1] the depth of a single feature and its surroundings; or, [2] depth differences between two or more dominant features. Although this method of width measurement does not substitute for direct, cross-sectioning of the sample, it does afford a means for comparing feature widths between two or more similar sites in a consistent, statistical manner.

The Width window includes a top view image and a histogram; depth data is displayed in the results window and in the histogram. The mouse is used to resize and position the box cursor over the area to be analyzed. The histogram displays both the raw and an overlaid, Gaussian-filtered version of the data, distributed proportionally to its occurrence within the defined bounding box.

Histogram

Raw Data

Histograms for depth data are presented on the bottom of the Width window. The histogram peaks correspond to the distribution of depths of analyzed regions of the image (see Figure 1).

Figure 1: Width Image and Corresponding Histogram

Correlation Curve

The Correlation Curve is a filtered version of the Raw Data Histogram and is represented by a red line on the Depth Histogram. Filtering is done using the Histogram Filter Cutoff parameter in the Inputs parameter box.The larger the filter cutoff, the more data is filtered into a Gaussian (bellshaped) curve. Large filter cutoffs average so much of the data curve that peaks corresponding to specific features are unrecognizable. On the other hand, if the filter cutoff is too small, the filtered curve may appear noisy.

The Correlation Curve portion of the histogram presents a lowpass, Gaussian-filtered version of the raw data. The low-pass Gaussian filter removes noise from the data curve and averages the curve’s profile. Peaks which are visible in the curve correspond to features in the image at differing widths.

Peaks do not show on the correlation curve as discrete, isolated spikes; instead, peaks are contiguous with lower and higher regions of the sample, and with other peaks. This reflects the reality that features do not all start and end at discrete depths.

When using the Widthview for analysis, each peak on the filtered histogram is measured from its statistical centroid (i.e., its statistical center of mass).

Width Procedure

Figure 2: Select Width from the workspace

	Or Right-click on a thumbnail in the Multiple Channel window and select Width. Or Select Analysis > Width from the menu bar. Or
	Click the Width icon in the NanoScope toolbar.
	The Width view, shown in Figure 3, appears showing results for the entire image.

Figure 3: The Width interface

Width Interface

The Width interface includes a captured image, Input parameters and Grid Markerdisplay, Results table, Guidelines and a Depth Histogram with grid markers, shown in Figure 4.

Figure 4: The Depth histogram

Width Parameters

The depth input parameters below define the slider cursor placement for determining the exact depth of a feature.

Table 1: Width Parameters

Three user-adjustable markers are placed on the depth histogram:

Table 2: Grid Markers

Table 3: Results Parameters

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