The energy of the valley splitting at both a conventional silicon metal-oxide-semiconductor (MOS) and a Si/SiGe interface is typically several hundred microelectron volts 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 and its magnitude can be tuned by controlling the gate electric field. It is known that the physical origin of the valley splitting results from the coupling of valley generated states due to the breakdown of the translational symmetry and the resultant momentum dispersion of electrons. Valley splitting in a silicon has been widely studied two dimensional electron systems (2DESs) 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, quantum dots (QDs) 32, 33 and dopants 34, 35. Recently, “valleytoronics”, which utilize valley degrees of freedom to create new functions, have been attracting much attention 12, 13, 14, 15, 16.
The distribution of the injected carriers is controlled by the front gate (FG) and the back gate (BG). These contacts are used to inject electrons (n-type) or holes (p-type) into an undoped SOI channel. The device has n- and p-type doped contacts. (b) Device cross-section and experimental configuration with TEM image of SIMOX gated p-i-n MOS diode. Valley splitting 2Δ is defined in the bottom right schematic, where the Fermi surface of contact is shown as an orange line that aligns with the antibonding state (fully valley polarized). The top right schematic illustrates the equi-energy surface of conduction minima states, where m l and m t are the longitudinal and transverse effective mass of the conduction electrons, respectively. Even for finite valley coupling, the main components of the envelope function in momentum space stay around +k 0 and -k 0. For strong confinement conditions, the two-fold degenerate valleys couple and form bonding and antibonding states because of the significant momentum dispersion. In quantum well, two-fold degenerate valleys take ground states and the residual four-fold degenerate valleys are lifted. (a) Energy dispersion of conduction band (CB), heavy hole (HH), light hole (LH) and upper band (UB) along.
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