An investigation of the valley splitting in n-channel silicon 〈100〉 inversion layers

Nicholas, R.J.; Klitzing, K. von; Englert, Th.

doi:10.1016/0038-1098(80)90628-6

Cited by 36 publications

(22 citation statements)

References 17 publications

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“…The gap value, its linear dependence on substrate bias [5], and its insensitivity to parallel magnetic field [8] are consistent with single-particle theoretical considerations for an asymmetric potential well that contains a 2D electron gas [9,10].…”

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confidence: 73%

“…However, this is the strongly interacting limit in which existing theories are not valid and, therefore, they cannot be directly applied to silicon MOSFETs. The origin of the excitations for the valley splitting is unknown so far.Experimental investigations of the valley splitting were performed largely [3] at high filling factor ν ≥ 9 based on analysis of the beating pattern of Shubnikov-de Haas oscillations in tilted magnetic fields [4,5,6,7]. The gap value, its linear dependence on substrate bias [5], and its insensitivity to parallel magnetic field [8] are consistent with single-particle theoretical considerations for an asymmetric potential well that contains a 2D electron gas [9,10].…”

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confidence: 70%

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Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

2003

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Using magnetocapacitance data, we directly determine the chemical potential jump in a strongly correlated 2D electron system in silicon when the filling factor traverses the valley gap at ν = 1 and ν = 3. The data yield a valley gap that is strongly enhanced compared to the single-particle value and increases linearly with magnetic field. This result has not been explained by existing theories.PACS numbers: 71.30.+h, 73.40.Qv A two-dimensional (2D) electron gas in (100)-silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) is a unique double-layer electron system with strong interlayer interactions. Indeed, the valley index is identical with the isospin quantum number, and one can therefore try to apply to this system a good deal of recent theoretical work on double-layer electron systems. In a double-layer system with small layer separation compared to the interelectron distance in either layer, strong interlayer correlations are predicted to give rise to the appearance of both novel ground states and novel excitations [1,2]. In quantizing magnetic fields strong enough to fully polarize real electron spins, two cases as determined by the isospin system symmetry are discussed: (i) at finite layer separation the symmetry is U(1) corresponding to an "easy-plane" anisotropy and (ii) at vanishing layer separation the symmetry transforms to SU(2) and the anisotropy disappears. In the first (second) case the lowest energy charge-carrying excitations are merons (skyrmions) that are isospin textures with the charge e/2 (e), where e is the electron charge [1, 2]. There is little doubt that the valley splitting in the 2D electron system in silicon MOSFETs should be of many-body origin at least for lowest odd filling factors because the electron-electron interactions (and correlations) in this system are strong; particularly, in accessible magnetic fields, the Coulomb energy exceeds significantly the cyclotron energy. However, this is the strongly interacting limit in which existing theories are not valid and, therefore, they cannot be directly applied to silicon MOSFETs. The origin of the excitations for the valley splitting is unknown so far.Experimental investigations of the valley splitting were performed largely [3] at high filling factor ν ≥ 9 based on analysis of the beating pattern of Shubnikov-de Haas oscillations in tilted magnetic fields [4,5,6,7]. The gap value, its linear dependence on substrate bias [5], and its insensitivity to parallel magnetic field [8] are consistent with single-particle theoretical considerations for an asymmetric potential well that contains a 2D electron gas [9,10].In this paper, we perform, for the first time, lowtemperature measurements of the chemical potential jump across the valley gap at the lowest filling factors ν = 1 and ν = 3 in a 2D electron system in silicon using a magnetocapacitance technique. The valley splitting is found to exceed strongly the single-particle value, decaying with filling factor. Unexpectedly, the data are best described by a linear inc...

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confidence: 73%

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confidence: 70%

Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

2003

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“…lifting of the degeneracy. This effect has been observed experimentally in Shubnikov-de Haas oscillation measurements in high magnetic fields 4,5,6,7,8,9,10,11 with energy splitting up to a few meV. Boykin et al presented a tight-binding model of the ground state splitting in a biased square quantum well with both hard-wall and cyclic boundary conditions 12,13,14 .…”

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confidence: 98%

Intervalley splitting and intersubband transitions inn-typeSi∕SiGequantum wells: Pseudopotential vs. effective mass calculation

2007

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Intervalley mixing between conduction band states in low-dimensional Si/SiGe heterostructures induces splitting between nominally degenerate energy levels. The symmetric double-valley effective mass approximation (DVEMA) and the empirical pseudopotential method (EPM) are used to find the electronic states in different types of quantum wells. A reasonably good agreement between the two methods is found, with the former being much faster computationally. Aside from being an oscillatory function of well width, the splitting is found to be almost independent of in-plane wave vector, and an increasing function of the magnitude of interface gradient. Whilst the model is defined for symmetric envelope potentials, it is shown to remain reasonably accurate for slightly asymmetric structures such as a double quantum well, making it acceptable for simulation of multilayer intersubband optical devices. Intersubband optical transitions are investigated under both approximations and it is shown that in most cases valley splitting causes linewidth broadening, although under extreme conditions, transition line doublets may result.

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“…Experimental research on the valley splitting, on the other hand, was conducted mainly on the Si metaloxide-semiconductor field-effect transistors (MOSFETs), in which the disorder effect is strong and direct measurement of the valley splitting proves to be difficult [5,6]. More than a decade ago, the introduction of the graded buffer scheme significantly improved the sample quality of the Si/SiGe heterostructures [7].…”

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confidence: 99%

Valley splitting ofSi∕Si1−xGexheterostructures in tilted magnetic fields

Lai

Pan

et al. 2006

Phys. Rev. B

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We have investigated the valley splitting of two-dimensional electrons in high quality Si/Si1−xGex heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor ν = 3 (∆3) is significantly different before and after the coincidence angle, at which energy levels cross at the Fermi level. On both sides of the coincidence, a linear density dependence of ∆3 on the electron density was observed, while the slope of these two configurations differs by more than a factor of two. We argue that screening of the Coulomb interaction from the low-lying filled levels, which also explains the observed spin-dependent resistivity, is responsible for the large difference of ∆3 before and after the coincidence.

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An investigation of the valley splitting in n-channel silicon 〈100〉 inversion layers

Cited by 36 publications

References 17 publications

Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

Strong enhancement of the valley splitting in a two-dimensional electron system in silicon

Intervalley splitting and intersubband transitions inn-typeSi∕SiGequantum wells: Pseudopotential vs. effective mass calculation

Valley splitting ofSi∕Si1−xGexheterostructures in tilted magnetic fields

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