 Solution

A gallium arsenide/aluminium gallium arsenide semiconductor heterostructure combines lower-gap GaAs with a higher-gap AlGaAs barrier. In a modulation-doped design, AlGaAs donors supply electrons to lower conduction-band states on the GaAs side. An undoped spacer separates the channel from ionized donors and reduces impurity scattering. The interface barrier and band bending quantize motion normal to the interface while allowing in-plane motion: a two-dimensional electron gas.

The normal confining potential is commonly triangular and finite rather than an infinite square well. At suitable density and low temperature, only the lowest normal subband is occupied. modulation doping reduces an important scattering source; it does not eliminate all disorder.

Use negatively biased surface gates to deplete the surrounding electron gas and leave a rectangular central region. Gate voltage controls lateral dimensions and barrier heights. Two constrictions can weakly couple the region to reservoirs, with a plunger gate controlling population. Etched boundaries are possible but may introduce edge disorder. A flat interior and steep edges approximate a box, givingFringing fields, finite barriers and penetration change the ideal result. A 2DEG confines only the normal direction; gates supply the extra lateral confinement. Gate-dependent spectroscopy can test level spacings, while charging measurements separate orbital confinement from Coulomb blockade.