Dimensional excitations in narrow electron inversion channels on Si

Electronic excitations in periodic arrays of isolated electron inversion channels on Si are studied in the far-infrared frequency domain at liquid-helium temperatures. A versatile dual-gate device allows one to tune the width of the channels $W$, their electron density, and the depth of the lateral confining potential nearly independently via field effect. In sufficiently wide channels ($W=1.5\mathrm{}$ μm) up to four-dimensional resonances with wave vectors $k_n=\frac{n\pi }{W}$ and odd $n$ characteristic for a single-electron channel are observed and well described by a classical theory. With $W$ decreasing below 100 nm we study the transition from classical to quantum confinement.