Theoretical examination of the quantum-size effect in thin grey-tin films

A theoretical treatment of the thin-film size quantization of grey-tin is presented. The energy levels describing the band gap are calculated as a function of film thickness. The calculation employs the linear combination of atomic orbitals method to construct the appropriate wave functions and considers the effect of the surface and interface electronic structure. The results compare favorably with experiment. The band gap is found to have a maximum value of approximately 430 meV for a film thickness of 40 A. The influence of the electronic structure due to the film boundaries is examined and shown to be important in order to examine the various experiments on the properties of the quantum-size effect.