[eng] We report here bands structure and the effective mass, in the direction of growth and in plan of HgTe (d 1 = 4.5 nm)/ CdTe(d 2 =4.8 nm) superlattice done in the envelope function formalism. We investigated Hall Effect with the help of the density of states and the Fermi level as a function of temperature. We found that temperature generated transitions from quasi bidimensional holes (Q2D) to three dimensional (3D) electrons and p type to n type conductivity respectively. When T increases, E g increases and the cut-off wavelength λ c decreases, with 5.06 μm <; λ c <; 6.3 μm and the cut-off frequency 47 THz <; f c <; 59 THz. This sample can be used as a mid infrared terahertz detector. This superlattice is better than the random alloy Hg 0.72 Cd 0.28 Te for application as infrared detector at 21.88 K. These results are a guide for the design of infrared nanostructures detectors.