Valley degeneracies in (111) silicon quantum wells

Abstract

(111) Silicon quantum wells have been studied extensively, yet no convincing explanation exists for the experimentally observed breaking of 6 fold valley degeneracy into 2 and 4 fold degeneracies. Here, systematic sp 3 d 5 s * tight-binding and effective mass calculations are presented to show that a typical miscut modulates the energy levels which leads to breaking of 6 fold valley degeneracy into 2 lower and 4 raised valleys. An effective mass based valley-projection model is used to determine the directions of valleyminima in tight-binding calculations of large supercells. Tight-binding calculations are in better agreement with experiments compared to effective mass calculations. DOI : **** PACS numbers: ******* Silicon nanostructures exhibit a plethora of interesting physical phenomena due to the 6 fold valley degeneracy of the bulk conduction band. Silicon devices are being pursued for spin based quantum computing 1 and spintronics 2 due to their scaling potential and integratability within the industrial nanoelectronic infrastructure. Relative energies and degeneracies of spin and valley states are critical for device operation in these novel computing architectures 1,2 , and conventional metal−oxide−semiconductor field−effect transistors (MOSFETs) that often involve the formation of a 2 dimensional electron gas (2DEG) at the semiconductorinsulator interface. Valley degeneracy of the 2DEG is highly dependent on the interface orientation. (100) Si quantum wells (QWs) show lower 2 fold and raised 4 fold valley degeneracy while (110) Si QWs show lower 4 fold and raised 2 fold valley degeneracy. The origin of these valley degeneracies is well understood and the experimental observations are in agreement with the effective mass based theoretical predictions 3 .Valley degeneracy in (111) Si QWs should be 6 according to standard effective mass theory. Experimental measurements on (111) Si/SiO 2 MOSFETs, however, show a conflicting valley degeneracy of 2 and 4 3-5 . 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. 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. Through systematic tight-binding calculations of flat and miscut (111) Si QWs we show that the surface miscut leads to the 2-4 degeneracy breaking and resolve the conflict between theory and experimental observations. To reduce the computational burden associated with searching the whole Brillouin-zone for valley minima, an effective mass based valley-projection model 10 tailored to miscut (111) surfaces is used. ...

Tight-binding analysis of the electronic structure of dilute bismide alloys of GaP and GaAs

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Valley degeneracy in biaxially strained aluminum arsenide quantum wells

“…Miscut samples are prevalent in the literature, for example (111) GaAs/AlAs growth has been shown to have superior morphology with a miscut angle from 0.5 • to 4 • and in general, intentional miscuts improve growth quality due to slip-step growth [69][70][71][72] . In Si, recently investigated hydrogen terminated (111)Si miscut surfaces have shown very high mobility 73 and the wafer miscut is expected to break the valley degeneracy 43,74 .…”

On the Validity of the Top of the Barrier Quantum Transport Model for Ballistic Nanowire MOSFETs

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