Particle diameter, signal-to-noise ratio and beam requirements for extended Rayleigh resolution measurements in the scanning electron microscope

Abstract

The extended Rayleigh resolution measure was introduced to give a generalized resolution measure that can be readily applied to imaging and resolving particles that have finite size. Here, we make a detailed analysis of the influence of the particle size on this resolution measure. We apply this to scanning electron microscopy, under simple assumption of a Gaussian electron beam intensity distribution and a directly proportional emitted signal yield without detailed consideration of scattering internal to the sample, other than being proportional to the sample thickness. From this, we produce beam-width normalized characteristics relating the particle diameter and resolution measure, while also taking consideration of the reduced signal yield that occurs from smaller particles. From our analysis of these characteristics, which we fit to experimental image data, we see that particle diameters <0.7 times the beam 1/e full width, d, give agreement better than 10% with the true extended Rayleigh resolution. Furthermore, we consider the signal current that must be collected to reliably distinguish between the mid-gap and peak intensity regions in the particle images. This leads to a practical guide that the signal-to-noise ratio (SNR) occurring between large area, continuous regions made of the same materials as the particle and background should typically be 10–30 times greater than the SNR that is desired to be achieved between the peak and mid-gap regions of just resolved adjacent identical particles having diameters in the size range 0.4–0.7d.