Temperature-driven photoconductivity spectra are studied in HgCdTe thin films and quantum well (QW) heterostructures grown by molecular beam epitaxy (MBE). It is shown that the absorption edge steepness in narrow gap HgCdTe epilayers approaches the fundamental limit. The corresponding Urbach energy is 1.5 to 4 meV at 4.2 to 77 K, which is an order of magnitude lower than values reported previously, indicating a significant progress in the quality of structures grown by MBE. Auger-suppressed multi-QW heterostructures that can be used for development of long-wavelength lasers/detectors are shown to have the comparable steepness of the absorption edge. The corresponding “Urbach” energy is much less than the threshold energy of the Auger recombination, which means that furthering the operating wavelengths beyond 20  μm is feasible for optoelectronic devices based on HgCdTe structures.