A ZnO/Mg0.2Zn0.8O heterostructure was characterized at T=2 K through capacitance measurements with using a conducting polymer, poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS), as a Schottky contact. The Nyquist diagram, which is the trajectory curve of the complex impedance vector, appeared to be an excellent semicircular shape, implying that the PEDOT:PSS/ZnO/Mg0.2Zn0.8O junction can be described with an equivalent single RC parallel circuit. Capacitance-voltage characteristics elucidate the existence of a two-dimensional electron gas, where 1019 cm-3 electrons are confined within 5 nm at the ZnO/Mg0.2Zn0.8O heterointerface.