Energy dependence of the effective mass in the envelope-function approximation

Results of a study on the tunneling electron effective mass as a function of energy and barrier width are reported. A system with a highly selective transmission factor, a double barrier, has been chosen in order to be able to define a particular energy. As the energies of the resonant transmission peaks are mostly determined by the effective mass of the material forming the well, while the transmission-peak width mostly depends on the barrier effective mass, both masses are obtained separately by fitting results for transmission using layers of periodic lattices and using the simplification allowed by the effective-mass approximation. The central well width has been varied and several transmission maxima have been considered, thus covering a wide energy range. The effective-mass in the relatively large barrier is shown to be much lower than the bulk-conduction-band value. For very thin barriers, when the decay length of tunneling electrons becomes of the same order as the barrier width, an anomalous increase in the effective mass is observed for high energies. Finally, we obtain the behavior of the effective mass as a function of energy in a one-dimensional triangular potential profile.