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In semiconductor devices that are the backbone of modern technology the conducting electrons are often confined by field effect or doping near an interface potential barrier and form a quasi-two-dimensional electron system. High resolution lithography and refined etching techniques now make it possible to laterally confine such originally two-dimensional electron systems to narrow channels with widths comparable to the de-Broglie wavelengths of the electrons. The transition from two-dimensional to one-dimensional electronic behavior that occurs as lateral confinement lengths are lowered to about 100 nm is directly observed with infrared spectroscopy of the electronic excitations in laterally microstructured metal-oxide-semiconductor and semiconductor-heterojunctions devices.
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J. P. Kotthaus (1987) studied this question.
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