Abstract
Many previous studies have handled the problem of the Quantum Size Effect `QSE' in connection with slab-shaped thin films. But real films do not always approximate an ideal slab sufficiently closely and in some cases wedge shapes are expected. In the first chapter the problem of QSE is reviewed in the case of slab-shaped films. In subsequent chapters the effect of shape on the density of states under size quantisation conditions is considered using the free electron approximation. The electron states in ideal and truncated wedge-shaped thin films is found from the computation of zeros of Bessel functions and their cross products respectively. It is found that the two-dimensional character of the density of states remains but with a modification of the step form occurring at the bottom of sub-bands of an ideal slab shape. In both ideal and truncated wedges an expression for the two-dimensional density of states is given. The singularity in this function at a sub-band edge is of a square root form for both cases and of equal weight. However, an additional singularity, also of a square root form, happens in the case of the truncated wedge whose ratio, , of the inner to the outer radii is not too great. This singularity occurs at a critical wavevector which depends on . The limit of a truncated wedge tending to a slab is investigated, and it is shown that the density of states tends to the result expected of a slab. (D71455/87)