Practical Electron Microscopy and Database

Fresnel fringes in TEM images, commonly observed in transmission electron microscopy (TEM), are highly sensitive to specimen thickness. These fringes arise from the interference of the electron wavefront as it encounters abrupt changes in specimen potential or geometry, such as edges or interfaces. The contrast and spacing of Fresnel fringes are influenced by the phase shifts from the electron beam, which are in turn dependent on the local thickness of the sample. Thicker regions generally induce more complex phase modulation, resulting in broader and less distinct fringes, while thinner regions tend to produce sharper and more pronounced fringe patterns. Therefore, Fresnel fringe behavior can serve as a qualitative, and in some cases semi-quantitative, indicator of local thickness variations, contributing to the analysis of structural and interfacial features in TEM imaging.

The spacing of Fresnel fringes in TEM is influenced by several factors, including the electron accelerating voltage, the mean inner potential (MIP) of the material, the defocus value, and the coherence of the electron beam. Although there is no universal table for Fresnel fringe spacing due to these dependencies, empirical observations, in Table 1929, under typical imaging conditions — such as 200 kV acceleration voltage and moderate underfocus — allow for approximate estimates. For silicon, which has a mean inner potential of approximately 12 V, the typical fringe spacing is in the range of 20 to 30 nm. Materials with higher MIP values, such as gold (~25 V) and tungsten (~30 V), tend to produce more closely spaced fringes, often in the range of 8 to 15 nm. In contrast, materials with lower MIP values, such as silicon dioxide (~10 V), show broader fringe spacing around 30 to 40 nm. These fringe spacing values provide a practical reference for estimating sample thickness in wedge-shaped specimens, especially when combined with knowledge of the sample’s maximum thickness and the total number of visible fringes.

Table 1929. Approximate Fresnel Fringe Spacing for Common Materials in TEM at ~200 kV.

In practice, anticontaminator is often used to minimize carbon (C) contamination which increases the thickness of the specimen and thus makes the observation of the fringe more difficult.