We propose a transfer matrix formalism of the triple-band, effective-m
ass equation to describe the transport process of carriers through an
arbitrary structure with layers of different materials. We use the coh
erent tunnelling approach in the flat band approximation. Special atte
ntion is paid to the boundary conditions. The triple-band matrix forma
lism is applied to AlAs/GaAs resonant tunnelling diodes and n- and p-t
ype InAs/AlSb/GaSb resonant interband tunnelling diodes. We compare th
e results of the single- and double-band effective-mass equation with
the triple-band effective-mass equation. We show that the influence of
the non-parabolicity of the bands on the position of the energy level
s in the quantum well for the simple resonant tunnelling structure is
of the same order as the shifts induced by the charging of the quantum
well. In the case of the p-type resonant interband tunnelling diode,
we calculate that the effect of the split-off band is not negligible.