Dimensional reduction effect on momentum of carrier electrons in nanoscale silicon materials

The momenta of carrier electrons in three-dimensional bulk silicon and low-dimensional silicon nano-structures have been analyzed by means of first-principles Kohn-Sham orbitals. Quantum-mechanical expectation values of the momentum of electrons in the conduction band have been calculated with respect to k coordinate, and the dimensional confinement has been discussed based on the behavior of the momentum. The conduction-band structure of silicon(001) nanosheet with about 5 nm thickness traces back to the multivalley one of bulk silicon in terms of the momentum state, while the momentum state for less than 2 nm cannot connect with that of bulk silicon.