= Solution
A <two-dimensional electron gas> is confined into discrete subbands perpendicular to an interface while retaining nearly free motion in its plane. It is not a literal zero-thickness <electron> sheet. In a <GaAs>/<AlGaAs> <semiconductor heterostructure>, the <band offset> and self-consistent <band bending> confine <electrons> on the <GaAs> side. Donors in <AlGaAs> can supply <electrons> while an undoped spacer separates them from the ionized dopants, reducing impurity scattering. This modulation-doping arrangement yields a high-mobility channel, with the lowest confinement subband occupied when the confinement spacing exceeds the Fermi and thermal scales. Gates tune the density or locally deplete the channel into constrictions. Low-temperature Hall and longitudinal measurements test the resulting sheet density and transport quality.
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