Determination of mean free path for energy loss and surface oxide film thickness using convergent beam electron diffraction and thickness mapping: a case study using Si and P91 steel

Abstract

SummaryDetermining transmission electron microscope specimen thickness is an essential prerequisite for carrying out quantitative microscopy. The convergent beam electron diffraction method is highly accurate but provides information only on the small region being probed and is only applicable to crystalline phases. Thickness mapping with an energy filter is rapid, maps an entire field of view and can be applied to both crystalline and amorphous phases. However, the thickness map is defined in terms of the mean free path for energy loss ( λ ), which must be known in order to determine the thickness. Convergent beam electron diffraction and thickness mapping methods were used to determine λ for two materials, Si and P91 steel. These represent best-and worst-case scenario materials, respectively, for this type of investigation, owing to their radically different microstructures. The effects of collection angle and the importance of dynamical diffraction contrast are also examined. By minimizing diffraction contrast effects in thickness maps, reasonably accurate ( ± 15%) values of λ were obtained for P91 and accuracies of ± 5% were obtained for Si. The correlation between the convergent beam electron diffraction-derived thickness and the log intensity ratios from thickness maps also permits estimation of the thickness of amorphous layers on the upper and lower surfaces of transmission electron microscope specimens. These estimates were evaluated for both Si and P91 using cross-sectional transmission electron microscopy and were found to be quite accurate.

An experimental method for calibration of the plasmon mean free path

“…The drop in λ(β) is very significant for β < 20 mrad and could be as high as 40%. For larger collection semi‐angles, the change will be more moderate, perhaps of the order of 10% in the range of 20 mrad < β < 157 mrad (Nakafuji et al , 2001; Lee et al , 2002; Mitchell, 2006).…”

Thickness measurements with electron energy loss spectroscopy

“…(1) and (2) agrees with the experiment only for small collection angles (b < 20 mrad). A saturation, not included in the model, is observed experimentally for larger b (see e.g., Crozier, 1990;Lee et al, 2002;Malis et al, 1988;Mitchell, 2006;Nakafuji et al, 2001;Ohshima et al, 2004;and Fig. 2 discussed below).…”

“…The apparent simplicity of this model makes it one of the most popular tools of thickness measurements by EELS (see e.g., Crozier, 1990;Egerton and Chen, 1987;Lee et al, 2002;Malis et al, 1988;Mitchell, 2006;Nakafuji et al, 2001;Ohshima et al, 2004;Yang and Egerton, 1995). Two modifications of this method can be distinguished, ''relative'' and ''absolute.…”

“…Lines in Figure 2 present simulation which is discussed in Angular dependence of the inelastic mean free path section. Diffraction effects are especially important in angular-dependent measurements as they can modulate the EELS intensity (Mitchell, 2006;Nakafuji et al, 2001) and thus result in overestimation of k by up to 25% (Yang and Egerton, 1995). Therefore, measurements summarized in Figure 2 were performed on amorphous SiO 2 .…”

“…On the contrary, EELS methods are much easier and faster both in acquisition and analysis. They do not require specific crystalline structure and work in a wide thickness range ($15-500 nm, see e.g., Mitchell, 2006;Egerton and Chen, 1987). However, the resulting energy-loss spectra are rather indirectly related to the thickness, and thus the technique has lower trust among many electron microscopists.…”