We show that, contrary to what would be expected on the basis of the mass barrier model, the transmission probability for the one-dimensional scattering problem with position-dependent mass normally tends to unity as energy goes to infinity, provided the mass is a continuous function of position.

Sassoli de Bianchi, M. & Di Ventra, M. (1998). A remark on the high-energy limit of the one-dimensional scattering problem with position dependent mass. Solid State Communications 106, pp. 249-251. Doi: 10.1016/S0038-1098(98)00073-8.