  We investigate the gate voltage dependence of capacitance of a system gate -
2D electron gas (C-Vg). The abrupt drop of capacitance at decreasing
concentration was found. The possible reasons of this drop, namely
inhomogeneity of electron density distribution and serial resistance of 2D
electron gas are discussed. Simultaneous analysis of gate voltage dependences
of capacitance and resistance has shown that in heavily doped 2D systems the
main role in the drop of capacitance at decreasing concentration plays the
resistance of 2D gas. It is found that the investigated systems remains
homogeneous down to the low temperature conductivity about (10^-2-10^-3)e^2/h.

Mesoscale and Nanoscale Physics;Disordered Systems and Neural Networks