LAUSR

A constant theme spanning the history of the scanning electron microscope (SEM) has been improving spatial resolution. Recent developments in SEM instrumentation (e.g., the thermal field emission gun, low aberration objective lenses, low beam energy operation with landing energy below 1 keV, and especially contamination control) have made achieving resolution in the sub-nm range routinely possible for solving many important problems [1]. However, the challenge which is often overlooked that may limit success is the problem of establishing the “visibility” of the features of interest. Indeed, for objects that produce low contrast, the visibility problem may be so severe as to impede finding the objects of interest, especially if searching of large areas for rare objects is required. This is not a newly recognized problem. Early in the history of the SEM, a “threshold equation” for establishing the visibility of features in SEM imaging was developed, based upon the empirically-measured Rose criterion for the “average observer” to detect features in noisy images [2, 3]. This SEM threshold equation relates the object contrast, Cct: Cct = (S SB)/S (1) where S is the beam-induced signal produced by a feature above the local background, SB, to the critical instrument parameters, beam current (iB), pixel dwell time (τ), and overall detection efficiency (ε, the yield of secondary electrons (SE) or backscattered electrons (BSE) per incident beam electron multiplied by the detector collection and signal conversion efficiency): iB (Threshold) > 4x10 A/(Cct ε τ) (2) For given values of τ and ε, specifying Cct in Eqn. 2 provides an estimate of the threshold (minimum) beam current needed to establish visibility for that level of contrast. Alternatively, if the beam current is specified, Eqn. 2 gives the threshold level of contrast for which visibility can be established. Thus, for any set of instrumental parameter choices (τ, ε, and iB), there will always be a threshold level of contrast below which features will not be visible. Because threshold visibility is subjective due to the acuity of the observer, Eqn. 2 should be thought of as producing imprecise “gray numbers”. Threshold visibility has also been found to depend on the object size (relative to the image field) and shape [4]. For the same level of contrast, an observer is better at recognizing extended objects that cover a large fraction of the field, e.g., a fiber that crosses most of the image field, than at finding small objects, e.g., an equiaxed particle that represents only a few percent of the image area.