Size quantization of surface-state electrons on the Si(001) surface

One-dimensional (1D) quantum wells are created on a $\mathrm{Si}\mathrm{}\left(001\right)\mathrm{}-c(4\mathrm{}\times 2)$ surface. A pair of straight Al ad-dimer chains works as potential walls for the confinement of surface-state electrons on the Si(001) surface. The quantum properties of the 1D quantum wells are directly probed by low-temperature scanning tunneling microscopy and spectroscopy. They are well described by size quantization of electrons in the unoccupied ${\pi }^{*}$ surface states of the $\mathrm{Si}\mathrm{}\left(001\right)\mathrm{}-c(4\mathrm{}\times 2)$ surface, based on the “1D particle-in-a-box” model.