A new method of self-consistent quantum calculation of the density of the space charge near the surface of a crystal is carried out for the semiconductor with nonparabolic (Kane) dispersion law of bands. The remarkable feature is the solution of the Schrodinger equation for electrons and holes in the energy range, including both bound energy states and states in the continuum. Theoretical voltage-capacitance dependence is calculated and coincides with experimental data. The dependence of the electron mass and surface mobility from the value of surface potential are analyzed.