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...

We have fabricated and characterized a field-effect transistor in which an electric field is applied through an encapsulated vacuum cavity and induces a two-dimensional electron system on a hydrogen-passivated Si(111) surface. This vacuum cavity preserves the ambient sensitive surface and is created via room temperature contact bonding of two Si substrates. Hall measurements are made on the H-Si(111) surface prepared in aqueous ammonium fluoride solution. We obtain electron densities up to 6.5 × 10 11 cm −2 and peak mobilities of ∼ 8000 cm 2 /V s at 4.2 K.

Low-field magnetotransport measurements on a high-mobility ͑ = 110, 000 cm 2 / Vs͒ two-dimensional electron system on a H-terminated Si͑111͒ surface reveal a sixfold valley degeneracy with a valley splitting Յ0.1 K. The zero-field resistivity xx displays strong temperature dependence for 0.07Յ T Յ 25 K as predicted for a system with high degeneracy and large mass. We present a method for using the low-field Hall coefficient to probe intervalley momentum transfer ͑valley drag͒. The relaxation rate is consistent with Fermiliquid theory but a small residual drag as T → 0 remains unexplained. Two-dimensional electron systems ͑2DESs͒ with additional discrete degrees of freedom ͑e.g., spin, valleys, subbands, and multiple charge layers͒ have attracted recent interest due to the role of such variables in transport and in the formation of novel ground states in the quantized Hall regime. In particular, systems with conduction-band valley degeneracy display a rich parameter space for observing and controlling 2DES behavior. 1 Among multivalley systems, electrons on the ͑111͒ surface of silicon are especially notable because effective-mass theory predicts the conduction band to be sixfold degenerate, yielding a total degeneracy ͑spinϫ valley͒ of 12 in the absence of a magnetic field ͑B͒. Previous investigations of Si͑111͒ transport using metaloxide-semiconductor field-effect transistor ͑MOSFETs͒ with peak mobilities Ϸ 4000 cm 2 / Vs observed a valley degeneracy g v of 2 or 6, with the reduced degeneracy attributed to oxide-induced surface strain. 2,3Here we report transport data on a hydrogen-terminated Si͑111͒ surface ͑H-Si͑111͒͒ with very high mobility ͑ = 110, 000 cm 2 / Vs at temperature T = 70 mK and carrier density n s = 6.7ϫ 10 11 cm −2 ͒ with clear sixfold valley degeneracy, indicated by the periodicity of Shubnikov-de Haas ͑SdH͒ oscillations, isotropic low-B transport, and strong T dependence of the longitudinal resistivity xx , consistent with a large g v . 4 In addition, we present a method for using the reduced Hall coefficient r H ϵ xy / ͑B / en s ͒ in the B → 0 limit as a probe of valley-valley interactions, using a drag model of intervalley momentum transfer in multivalley 2DESs. We find that the Hall coefficient ͑and thus, by our model, the intervalley drag͒ becomes strongly suppressed at low temperatures ͑T Շ 5 K͒; furthermore, although the T dependence of the drag is roughly quadratic as expected from Fermi-liquid theory, a small residual drag in the T → 0 limit remains unexplained.To create and probe a high-mobility electron system on a bare surface, we fabricate a device similar to a four wire MOSFET, with the critical difference that we replace the Si-SiO 2 interface with a H-Si͑111͒ surface adjacent to a vacuum cavity. 5 The main processing enhancements in the device discussed here relative to our prior samples are a higher resistivity Si͑111͒ substrate ͑ ϳ 10 k⍀-cm͒ and final H-termination and bonding performed in an oxygen-free ͑Ͻ1 ppm͒ environment. 6 The resulting device has a very high mobility wh...