The influence of supporting grid bars on the temperatore increase of a thin fiim subjected to electron irradiation

Abstract

The heating effect of an incident electron beam may cause a material to be radiation-sensitive. For example, the adsorption behaviour of inert gases on graphite observed in a transmission electron microscope depends critically on the temperature of the substrate. Early consideration of beam heating dealt with a circular film illuminated at the centre by an electron beam of circular cross-section. In practice, however, the film is often supported across a square aperture and is not centrally illuminated. It has recently been shown that the method of images may be used to solve the problem of the heating of a square film of thermal conductivity k by a beam whose cross-section is entirely within the film. This solution has the advantage that it applies regardless of where the incident electron beam strikes the film. The general solution involves an infinite sum over a two dimensional lattice of heat sources and sinks. Though the sum is readily evaluated by means of a computer, it is helpful to consider a particular limiting case which is readily understood in terms of three images and the main beam. This case is illustrated in Figure 1.