The feasibility and fundamental difficulty in developing the infrared intersubband quantum cascade lasers in shorter wavelength range were discussed theoretically. The band offsets of InAs/AlSb on GaSb substrate, InAs/Al_0.6Ga_0.4Sb on GaSb substrate, and In_0.53Ga_{0 .47}As/In_0.52Al_0.48As on InP substrate, and the confined states of their quantum wells with and without an applied electric field were analyzed and calculated by using the fundamental assumption of model-solid theory, strained band structure theory, empirical-two-band model for non-parabolic band, and methods of propagation matrix and laminar approach. It was found that the greatest energy difference between subband edges can not exceed 56～62% of the conduction band offset, and will be decreased further by the indirect valley. A designed structure of intersubband quantum cascade laser consisting of 250 coupled quantum wells in 25 periods under electric field 100kV/cm for emitting the shortest wavelength 2.88μm was proposed.