A theory is given of the density of states (DOS) in the low-energy tail for the disordered two-dimensional electron gas (2D EG) in a semiconductor heterostructure subjected to Gaussian random fields of any origin (especially of short range). The calculation is carried out by means of a path-integral technique within the approximation based on a non-local harmonic modelled action and that of the ground-state contribution. A simple analytic expression for the 2D DOS and different variational equations for the curvature of the trial well are then obtained, which describe the DOS tail in explicit dependence on the potential correlator, i.e., on the disorder origin as well as the geometry of the realistic 2D EG. An interpolation scheme for obtaining the 2D DOS over the whole energy region is proposed. The DOS in the deep tail is found to roughly go as a decreasing exponential function whose exponent is proportional to |E|n with n varying from 1 to 2 for very short- and long-range potential correlations, respectively. The case of a Gaussian potential correlator is thoroughly examined.
