We study theoretically the energy spectrum of conduction electrons and the corresponding density-of- states function (DOS) of III–V, ternary and quaternary semiconductors, whose unperturbed energy band structures are defined by the three band model of Kane, in the presence of an external electric field. It has been observed that the unperturbed isotropic energy spectrum becomes modified under external electric field and changes into an anisotropic dispersion relation with the energy-dependent mass anisotropy. Besides, the band gap of semiconductors increases with the electric field; a phenomenon never explained earlier either theoretically (Franz–Keldysh effect) or experimentally. In addition, from the study of the DOS, it indicates that the carriers disappear from the edge of the conduction band after certain values of the applied electric field. It has been found taking n-InSb, n-InAs, Hg 1− x Cd x Te and In 1− x Ga x As y P 1− y lattice matched to InP as examples of Kane-type semiconductors for numerical computation that the increase of band gap and disappearance of carriers from the edges of the conduction band do happen for all types of materials in the presence of external electric field. The well-known energy spectrum and the corresponding DOS for wide-gap semiconductors in the absence of electric field have been obtained under certain limiting conditions from the theoretical expressions. This compatibility is an indirect mathematical test of our generalized analysis.