QUANTUM SIZE EFFECT IN CLEAN ALUMINUM FILMS

Abstract

In the modern world, there's a notable trend towards the active miniaturization of electronic devices. With technological advances enabling the manipulation of nanostructures, there's an increasing focus on exploring quantum effects pivotal to such designs. One distinguishing feature of nanostructures is the quantum nature of the electron's energy spectrum. This spectrum becomes discrete in directions where electrons move. Depending on the direction of this confinement, structures can be categorized as nanoplates, quantum wires, or quantum dots. The properties of such structures can significantly differ from those observed in large-scale systems. When discussing superconductivity, particular emphasis is placed on its macroscopic quantum properties.The influence on electronic wave functions is reflected in the characteristics of the superconducting state on broader scales. The Bardeen-Cooper-Schrieffer (BCS) theory is frequently utilized to analyze these nanostructures. The Gor’kov equations method serves as a potent tool for tasks related to the BCS theory. For instance, it can determine the parameters of the superconducting state, critical temperature, and current. Components of these equations, like Green's functions, are associated with various system properties. Research in the early stages of superconductivity studies revealed that the critical temperature (Tc ) – the temperature at which a material transitions to a superconducting state – can differ significantly between thin films and bulk materials. Intriguingly, reducing the film's thickness can both decrease (e.g., in niobium) and increase (e.g., in aluminum) the Tc value. This study delves into the quantum size effect in thin aluminum films, paving the way for materials with higher transition temperatures. Such advancements can simplify and make the maintenance of superconducting systems more cost-effective. In this study, a theoretical relationship between the critical temperature of a thin aluminum film and its thickness was derived. The Green's function method was chosen, which hadn't been previously employed for this computation. This approach offers greater potential compared to other superconductivity theory methods, presenting extensive avenues for theoretical exploration in this domain. The authors are confident that this work will contribute to further research on quantum dimensional effects in low-dimensional superconducting structures.