An accurate analytical approach to electron crystallography

A much more accurate analytical expression of dynamical electron diffraction than the phase object approximation (POA) formula has been derived in this paper which decreases the restriction of sample thickness up to almost one order of magnitude compared to POA theory. The importance of the new expression is twofold. First, a sample with such a thickness that new expression remains valid can be prepared experimentally. Second, the new expression reveals a clear and straightforward relationship between the wave function and crystal potential. In the expression, the effect of dynamical diffraction on wave function can be simply attributed to two factors TP(D)=(sin(λπzg2))/(4π2g2) and TA(D)=[1−cos(λπzg2)]/4π2g2. Compared to the effect of transfer functions of an electron microscope on wave function, we found that TP(d) and TA(d) play the same role as transfer function but are independent of the instrument. For this reason, we here call the former as “extrinsic transfer functions” and the latter as “intrinsic” ones. In principle, one should correct not only extrinsic transfer functions but also intrinsic ones if one desires to achieve higher resolution.