Rise Distance Method
Figure 2: (a) The calculated rise distance measurement for a given Ga ion beam and (b) the rise distance for the same Ga ion beam as Figure 2a, with random noise added.
Figure 3: An experimental rise distance measurement showing the fluctuations due to beam statistical noise. A sharp edge within a graphite specimen is being used here as a knife edge. At the location shown by the red arrow in the micrograph, the beam increases from 20 percent to 80 percent of its full value in a distance of 1.8 nm. Note the bright line at the edge at the right side of the micrograph (see discussion in the text).
and 15 measurements, respectively. For these data the average rise distance was 3.7 nm, and the variance was 0.3 nm. Te smallest rise distance, 2.75 nm, lies 3 standard deviations from the mean. Te probability of this would be about 1 part in 8,000, so the odds of finding a 2.8-nm rise distance are small.
The Case of Non-uniform Knife Edge Yet another problem with the rise distance measurement
comes from a non-uniformity of the knife edge and a consequent varying secondary electron yield. Consider an ion beam with current density distribution J(r) that strikes
30
a knife edge with a curved end of radius rc, as shown in Fig- ure 5. Te secondary electron yield depends strongly on the angle between the beam direction and the normal
to the
specimen surface. A simulation of the yield of secondary electrons from Si bombarded by 30 keV Ga+ ions was made by Ohya and Ishitani [6]. We used their results to calculate the effect on the rise distance measurement of the non-uniform secondary electron yield from the knife edge. We found that the results depend strongly on the relative magnitudes of the radius rc and the FWHM radius of the current density, as shown in Figures 6a and 6b.
www.microscopy-today.com • 2011 May
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