Electronic states and the Stark shift in narrow band InSb quantum spherical layer

Electron states and the Stark shift in narrow band quantum spherical InSb layers are considered in frameworks of Kane model with respect to non-parabolicity of the dispersion law. An exact analytical solution of the corresponding Klein-Gordon equation for the model of impenetrable walls is obtained, and in addition to that a transcendent equation for determination of electron energetic spectrum is derived as well. The influence of the electric field is considered in frames of the perturbation theory, it is also shown that the value of the Stark shift is proportional to the second power degree of the field. Dependences of the electron energy versus the internal field values, external radius, and electric field are presented. The obtained results are compared with results obtained for the case with standard dispersion.