The effect of energy bands on the amplification coefficient of Rayleigh waves in thin bismuth films is investigated quantum mechanically in the gigahertz frequency region. It is shown that the amplification coefficient for the modified non-ellipsoidal non-parabolic model is much closer than that for the non-ellipsoidal non-parabolic (NENP) model to that for the ellipsoidal parabolic model or the ellipsoidal non-parabolic model in the low-temperature limit. Therefore the NENP model in the thin bismuth films does not explain very well the electronic transport properties in the gigahertz region at very low temperatures.