Generally speaking, a specimen appropriate for TEM study should be thin enough for electron transmission and representation of the nature of the materials:
i) Thin enough to be treated as a weak phase object;
ii) Electron beam spreading (Refer to interaction volume) within the specimen is negligible.
However, the sample should also be thick enough so that:
i) It can represent the bulk material, which is studied, without significant effects from the two specimen surfaces
ii) Surface contamination does not dominate the signals (e.g. for HRTEM, STEM, EDS, and EELS)
iii) There is sufficient signal from scattering events to give signal to form images or spectra.
For a sample consisting of nano-particles, the specimen thickness can be estimated from their projected shape and size. Additional requirements for the TEM specimen of nano-particles:
The overall thickness of the specimen (including the supporting film and the nano-particles) can satisfy the basic thickness constraints listed above.
Additional requirements for FIB-prepared specimen:
i) The specimen is thick enough so that the unaffected materials can still represent the bulk material which is studied;
ii) Minimizing the amorphised layers on the two surfaces of the specimen.
Furthermore, the required specimen thickness also depends on the technique used for a specific analysis. For extremely high quality TEM analysis, refer to extremely high quality specimens. Although almost no actual specimens satisfy all these criteria mentioned above, the list can give you an idea to get close to the best achievable TEM analysis.