Abstract
The recent successful construction and testing of spherical rration correctors has lead to a renewed investigation of the appropriate image simulation algorithms and for detailed calculations to predict the imaging behaviour of these corrected instruments. In this thesis, the Generalized PCD approximation was developed to interpret the imaging behaviour at very near zero Cs. The thesis also gives the results of calculations under the multi-slice formalism with the inclusion of damping envelopes due to limited spatial and temporal coherence for both zero and small Cs values for Si [110] and GaN [010]. When the spherical rration coefficient is at zero, there exist a optimum focus range, and this range is related to both the shortest neighboring distance H and the Accelerating voltage. The higher the Accelerating voltage, the wider the optimum focus range, and the shorter the neighboring distance H, the narrower the focus range. The imaging behaviour near zero Cs is also investigated since the measurement on Cs has an error about 10%. The optimum focus shift when altering Cs values. This shifting behaviour is very sensitive to the exact Cs value because the defocus value should compensate the effect of the spherical rration in order to get good cancellation of the phase rration. Also, this behaviour is more pronounced for a structure with shorter dumbbell distance due to Cs phase shift rate proportional to the power fourth of H vector. For the condition of small Cs values, the resolution limit would be at the information limit due to the instrument instability and partial coherency. Furthermore, the contrast level near zero Cs is dominately due to defocus and nearly proportional to the defocus value. The Generalized PCD approximation provides a better prediction of near zero Cs imaging behaviour. Its agrees with the existence of optimum focus range and applicable range which is smaller than optimum focus Dfopt,.