The results are presented from an investigation of the transition temperature T-k and energy gap 2 Delta(0) as a function of the thickness of superconducting cold-deposited beryllium films. The transition temperature increases exponentially as the film thickness is decreased. In the interval of very small thicknesses a drop in T-k is observed. The thickness dependence of 2 Delta(0) is analogous to the dependence of T-k. In the investigated interval of thicknesses the ratio 2 Delta(0)/kT(k) = 3.6 +/- 0.1, indicating that the cold-deposited modification of beryllium is a superconductor with weak electron-phonon coupling. Superconducting beryllium films could only be produced up to thicknesses d(cr) similar to 200 angstrom. At thicknesses close to d(cr) a transition to the non-superconducting alpha phase is observed. The growth of the transition temperature with decreasing thickness is attributable to the influence of dimensional quantization of the transverse motion of electrons in the film. The drop in T-k for very small thicknesses (similar to 30 angstrom) is regarded as due to the influence of fluctuations. The functions T-k(d) obtained by various authors for thin films of other superconductors, such as Al, Sn, Bi, Ga, and Pb, are discussed.
