The resolution of photoelectron microscopes with UV, X-ray, and synchrotron excitation sources

Abstract

The resolution of emission electron microscopes is calculated by determining the intensity distribution in the image. The object is a small disc of uniform brightness centered on the axis. A finite object, as distinct from a point source, provides a non-zero current in the image without the requirement of infinite object brightness and the consequent infinities in the geometrical intensity distribution. The minimum object size, which in turn affects the resolution of the microscope, depends on the minimum current or contrast required in the image. In photoelectron microscopes with UV illumination just above the threshold for emission the predominant aberrations are the chromatic and spherical aberrations of the accelerating field and the spherical aberration of the objective lens. For higher energies, e.g. in the soft X-ray range, the chromatic aberration of the objective lens must also be taken into account, as the aberration coefficients of the accelerating field are greatly reduced. The intensity distributions in the image are calculated first for single energies. The intensity distribution for a beam with a range of energies is obtained by adding a series of single-energy distribution curves weighted according to the energy distribution function. In the presence of spherical aberration the position of the image formed by the electrons depends on the angle of emission. In image planes between the paraxial and marginal planes the combination of spherical aberration and defocus causes the image spot to have a retrograde type or behavior as the angle of emission increases. The image spot initially moves away from the axis in the azimuth of emission and then returns to the axis and moves away in the opposite azimuth. As a result the intensity in the central portion of the image plane is enhanced. The single-energy intensity distribution curves calculated as a function of depth in the image reveal the existence of a compact, high-intensity image peak in an image plane located between the paraxial and marginal planes. This peak occurs in the plane in which the image spot has a maximum retrograde displacement equal to its radius. The present analysis shows that the resolution in the high-intensity plane is better than in the plane of least confusion, and the effects of aberrations in these two planes are quite different. Resolution is best in the high-intensity plane for the smallest object satisfying the image requirements. As a practical example of this approach, the resolution for a UV photoelectron microscope in which the lens parameters are known and the emission current density and energy spread have been measured is calculated to be of the order of 5 nm. The resolution considerations of an ESCA microscope are discussed. A significant improvement in the resolution of emission electron microscopes would result from the use of corrected electron optics.