  We propose a simple analytical model to explain possible appearance of the
metallic conductivity in the two-dimensional (2D) LaAlO$_3$/SrTiO$_3$
interface. Our model considers the interface within a macroscopic approach
which is usual to semiconductor heterojunctions and is based on drift-diffusion
equations. The solution of these equations allows to obtain the positions of
band edges as a function of distances from the interface. We show that for the
2D metallic conductivity to appear at the interface, the constituting
substances should have the same type (either electronic or hole) of
conductivity; in the opposite case the possible transition to metallic phase
has a three-dimensional character. The results of our model calculations are in
agreement with available experimental data.
