Effects of the probe pattern on the aberration

In any electron optical system, compensating for the lens aberrations is the key to improving the spatial resolution. Ofall the dominant aberrations, only the spherical aberration and chromatic aberration continue to limit the performance ofmicroscopes. In the plane ofthe Gaussian image, these aberrations are given by: spherical aberration: o = Cs a chromatic aberration: o C a oV/V, Where C5 and C are the coefficients of spherical aberration and chromatic aberration, respectively. a is the divergent angle ofthe electron path with respect to the axis. 8V is the energy spread ofthe electron source and V is the electron energy, in eV. Several systems, such as a magnetic sextupole and quadrupole configuration [1,2], have been proposed to correct these aberrations. Recently, Crewe proposed a simple "mirror corrector" system for correcting them by reversing their coefficient signs [3]. However, it will be some time before any ofthese proposed systems will prove to be applicable on a practical basis. In the meantime, it may be profitable to concentrate on how to choose the best operating parameters for any existing system, in order to optimize the resolution. The resolution of a system is calculated by combining the effect ofthe dominant aberrations with the effects of diffraction and defocus: diffraction: 8d 0.6 lAJa, defocus: C5 a2c where X =(15O/V)' A isthe electron wavelength, and c is the defocus parameter, defined in this paper as 0 at the Gaussian image plane and 1 at the marginal plane. The optimum resolution is achieved by choosing a and to attain the minimum combined aberration. Conventionally, a is chosen to be the largest possible divergent angle, which is the angle determined by the aperture size. This considers only the worstcase situation and ignores the fact that the path of the optical ray is critically dependent on a. Simply because there are some large divergent angles does not mean necessarily that those contributions dominate the formation of the electron probe. Ignoring the possible range of a results in the loss of all the details of the probe pattern. This prevents one from deriving any information about the resolution from the internal details of the probe. Calculations based on a single, maximum value of a can be expected to be conservative and to underestimate the power of the microscope. Recently, Rempfer and Mauck investigated the interior intensity pattern of an electron probe by ray tracing the path ofeach individual electron[4J. Their results showed that the intensity distribution ofthe probe varied greatly in different defocus planes, and was extremely nonuniform in every plane. This paper presents a study in which a numerical simulation is used to determine the probe pattern resulting from the spherical aberration, chromatic aberration, source size, and defocus. The probe pattern in different defocus planes is then convoluted with two types of simulated samples in order to directly investigate the possible resolution. The results show that the conventional calculations ofresolution may not be appropriate for all circumstances. Also, the optimal operational parameter can be very different, depending on what information the operator wishes to get from the microscope.