A method for calculating the parameters of the space-charge region in a thin film of a semiconductor with Kane’s charge-carrier dispersion relation at room temperature is proposed. A self-consistent calculation scheme for solving the system of coupled Poisson, Klein-Gordon-Fock, and Schrödinger equations for mercury cadmium telluride is implemented. Exact solutions for the subband dispersion relations are obtained. Linearization of the coordinate dependence of the potential in thin films is demonstrated and limits on the applicability of the triangular-well approximation are established. The coordinate dependence of the potential and charge density and the capacitance-voltage characteristics calculated within the context of the effective-mass approximation and of phenomenological theory are compared and the limits of applicability of the phenomenological description of the space-charge region are determined. The influence of the heavyhole subsystem on the main characteristics of the space-charge region is revealed.