Monte Carlo Modelling of Secondary Electron Yield from Rough Surfaces

Abstract

Monte-Carlo programs are well recognized for their ability to model electron beam interactions with samples, and to incorporate boundary conditions such as compositional or surface variations which are difficult to handle analytically. This success has been especially powerful for modelling X-ray emission and the backscattering of high energy electrons. Secondary electron emission has proven to be somewhat more difficult, since the diffusion of the generated secondaries to the surface is strongly geometry dependent, and requires analytical calculations as well as material parameters. Modelling of secondary electron yield within a Monte-Carlo framework has been done using multiple scattering programs, but is not readily adapted to the moderately complex geometries associated with samples such as microelectronic devices, etc.This paper reports results using a different approach in which simplifying assumptions are made to permit direct and easy estimation of the secondary electron signal from samples of arbitrary complexity. The single-scattering program which performs the basic Monte-Carlo simulation (and is also used for backscattered electron and EBIC simulation) allows multiple regions to be defined within the sample, each with boundaries formed by a polygon of any number of sides. Each region may be given any elemental composition in atomic percent. In addition to the regions comprising the primary structure of the sample, a series of thin regions are defined along the surface(s) in which the total energy loss of the primary electrons is summed. This energy loss is assumed to be proportional to the generated secondary electron signal which would be emitted from the sample. The only adjustable variable is the thickness of the region, which plays the same role as the mean free path of the secondary electrons in an analytical calculation. This is treated as an empirical factor, similar in many respects to the λ and ε parameters in the Joy model.