Size effects on the thermodynamic properties of thin films

Although it is generally known that size effects can exist for thermodynamic properties like the internal energy and heat capacity, until now these effects have usually been neglected, as no simplified procedure for calculating such effects has been presented in the past. This paper presents an approach for estimating the size effects on the thermodynamic properties of thin films, which becomes especially prominent at cryogenic temperatures because of their dependence on the Planck distribution function. A size effect on the Debye temperature of thin films was previously observed, but the present analysis indicates that the Debye temperature is independent of the size of the specimen. A novel nondimensional parameter is also introduced that accurately describes the thermal behavior of thin films of different materials, and provides a clear demarcation between the microscopic and the macroscopic regimes for the thermodynamic properties. With this nondimensional parameter, the heal capacity for a thin film of any given thickness and any material can be easily calculated, provided the bulk heat capacity of the material is known at the temperature of interest.