We introduce an elementary model for the electrostatic self-consistent potential in a two-dimensional electron gas. By considering the perpendicular degree of freedom arising from the electron tunneling out of the system plane, we predict a threshold carrier density above which this effect is relevant. The predicted value agrees remarkably well with the onset for the insulator to quasi-metallic transition recently observed in several experiments in SiO2-Si and AlGaAs-GaAs heterojunctions.
@article{arxiv.cond-mat/9912457,
title = {A simple model for the metal-insulator transition in a two-dimensional electron gas},
author = {J. C. Flores and V. Bellani and F. Dominguez-Adame},
journal= {arXiv preprint arXiv:cond-mat/9912457},
year = {2007}
}