In electron field emission experiments, a linear relationship in plots of slope vs. intercept obtained from Fowler-Nordheim analysis is commonly observed for single tips or tip arrays. By simulating samples with many tips, it is shown here that the observed linear relationship results from the distribution of input parameters, assuming a log-normal distribution for the radius of each tip. Typically, a shift from the lower-left to the upper-right of a slope-intercept plot has been correlated with a shift in work function. However, as shown in this paper, the same effect can result from a variation in the number of emitters.
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