Integer Quantum Hall Effect on a Six-Valley Hydrogen-Passivated Silicon (111) Surface

Abstract

We report magneto-transport studies of a two-dimensional electron system formed in an inversion layer at the interface between a hydrogen-passivated Si(111) surface and vacuum. Measurements in the integer quantum Hall regime demonstrate the expected sixfold valley degeneracy for these surfaces is broken, resulting in an unequal occupation of the six valleys and anisotropy in the resistance. We hypothesize the misorientation of Si surface breaks the valley states into three unequally spaced pairs, but the observation of odd filling factors, is difficult to reconcile with noninteracting electron theory.PACS numbers: PAC Nos. 73.43.Qt, 71.70.Di The silicon field effect transistors (FETs) that are at the heart of contemporary microelectronics rely on mobile electrons or holes confined at the interface between Si and a higher bandgap barrier material. This barrier in metal oxide silicon (MOS) FETs is SiO 2 , an amorphous material which introduces inevitable disorder at the Si-SiO 2 interface and limits the carrier mobility in these devices. A crystalline interface can be created using epitaxial SiGe-Si layers in which mobilities can be over an order of magnitude higher than the best MOS-FET devices [1], but this technique is limited to the [100] oriented surfaces [2]. Recently a new technique for Si crystalline interfaces has been demonstrated [3] in which a Si interface is passivated with a monolayer of hydrogen and the barrier material is a vacuum. While the inertness and high degree of atomic perfection of these surfaces has been known for some time [4,5,6], the development of high mobility electronic devices on H-Si enables the exploration of two-dimensional (2D) physics of novel Si surface orientations and may one day allow quantum devices to be engineered at the atomic scale using surface manipulation techniques [7].We report here the first detailed magneto-transport studies of a 2D electron system (2DES) at a H-Si(111) surface gated through a vacuum barrier. Electron mobilities are an order of magnitude higher (24, 000cm 2 /Vs) than Si(111) MOSFETs, enabling the observations of the integer quantum Hall effect (IQHE). In the effective mass approximation the ground state for a 2DES on the Si(111) surface is six-fold degenerate with each Si conduction band valley contributing an equal number of carriers, (Fig. 1d) [8,9,10] and six [11,12] along with isotropic resistivities for both. Subsequent proposals [11,13] have tried to explain these anomalous observations, but to date conclusive experimental results are still lacking.The high mobility 2DES can be created by contact bonding two individual Si substrates [3] (Fig. 1a). One is the H-Si(111) substrate (float zone, p-type, ρ ∼ 10 Ω-cm) which has four phosphorous contacts forming a 1-mmwide square with sides oriented parallel to the [110] and [112] crystallographic directions (Fig. 1b and 1c). The second is a silicon-on-insulator (SOI) substrate which acts as the remote gate, where an electric field can be controlled within an etched cavity. The Si(111) surf...

Valley degeneracies in (111) silicon quantum wells

“…3 the step morphology of the QW surface modulates the wavefunction which in turn influence energy levels to give rise to Δ 2-4 splitting. A 0.2° miscut resembles closely to that of the xperiment 6 . The e L cell =264.07 nm and L y =0.38 nm long in x-and y-directions, respectively.…”

“…Experimental measurements on (111) Si/SiO 2 MOSFETs, however, show a conflicting valley degeneracy of 2 and 4 [3][4][5] . Recently 2-4 valley-splitting has also been observed in magnetotransport measurements performed on hydrogen terminated (111) Si/vacuum field effect transistors 6 . Previously proposed theory of local strain domains 4 can not explain this splitting since the Si-vacuum interface is stress free.…”

“…Previously proposed theory of local strain domains 4 can not explain this splitting since the Si-vacuum interface is stress free. The splitting is also unlikely to be a many-body phenomenon 7 .Careful imaging of the surface morphology shows the presence of mono-atomic steps (miscut) on the (111) Si surface 6,8 as well as at the Si/SiO 2 interface in (111) Si MOSFETs 8,9 . Atomistic models such as tight-binding are needed to accurately model the electronic structure of miscut QWs.…”

“…Careful imaging of the surface morphology shows the presence of mono-atomic steps (miscut) on the (111) Si surface 6,8 as well as at the Si/SiO 2 interface in (111) Si MOSFETs 8,9 . Atomistic models such as tight-binding are needed to accurately model the electronic structure of miscut QWs.…”

Using nanoscale transistors to measure single donor spins in semiconductors

“…A higher order analysis would require detailed investigation of the device specific interface and intrinsic contributions to the other scattering processes, and hence to the channel mobility and τ 0 . Related to this concern, the mobility of the 2DEG channel can be improved -e.g., by using hydrogen passivation to mitigate surface roughness at the oxide interface [11] -to increase ρ. We conservatively estimate a factor of 10 increase in ∆I/I 0 from such improvements.…”