The Fermi energy and in-plane electron effective mass are investigated as a function of film thickness and electron concentration. It is shown that in size quantized semiconductive films with arbitrary non-parabolicity of energy band the Fermi energy and in-plane effective mass has an oscillating behavior with respect to film thickness. The period of these oscillations is determined as a function of electron concentration. In the case of ultrathin films, these results are discussed in detail and compared with the experimental data on GaAs quantum wells. The results are in good agreement with the experimental data. (c) 2007 Elsevier B.V. All rights reserved.