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Multi-valley effective mass theory for silicon quantum well structure is studied taking into account the external fields and the quantum interfaces. It is found that the phenomenological delta function potential, employed to explain the…

Quantum Physics · Physics 2009-11-13 S. -H. Park , Y. Y. Lee , Doyeol Ahn

A sharp potential barrier at the Si/SiGe interface introduces valley splitting (VS), which lifts the 2-fold valley degeneracy in strained SiGe/Si/SiGe quantum wells (QWs). This work examines in detail the effects of Si/SiGe interface…

Materials Science · Physics 2012-03-07 Zhengping Jiang , Neerav Kharche , Timothy Boykin , Gerhard Klimeck

Electron spin-qubits in silicon-germanium (SiGe) heterostructures are a major candidate for the realization of scalable quantum computers. A critical challenge in strained Si/SiGe quantum wells (QWs) is the existence of two nearly…

Mesoscale and Nanoscale Physics · Physics 2025-11-20 Abel Thayil , Lasse Ermoneit , Markus Kantner

Silicon quantum dot qubits must contend with low-lying valley excited states which are sensitive functions of the quantum well heterostructure and disorder; quantifying and maximizing the energies of these states are critical to improving…

We present the theory and measurement of valley splitting in a quantum point contact (QPC) in a modulation doped Si/SiGe heterostructure. Our measurements are performed on a submicron Schottky-gated device. An effective mass theory is…

Mesoscale and Nanoscale Physics · Physics 2010-03-30 L. M. McGuire , Mark Friesen , K. A. Slinker , S. N. Coppersmith , M. A. Eriksson

Electron spin qubits in Si/SiGe quantum wells are limited by the small and variable energy separation of the conduction band valleys. While sharp quantum well interfaces are pursued to increase the valley splitting energy deterministically,…

We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter, $v_v$, which encapsulates the physics of the quantum well…

Materials Science · Physics 2013-08-26 Mark Friesen , Sucismita Chutia , Charles Tahan , S. N. Coppersmith

The coupling between $z$ valleys in the conduction band of a Si quantum well arises from phenomena occurring within several atoms from the interface, thus ruling out a theoretical description based on pure effective mass theory. However,…

Mesoscale and Nanoscale Physics · Physics 2013-08-26 Sucismita Chutia , S. N. Coppersmith , Mark Friesen

The bandstructure of bulk silicon has a six-fold valley degeneracy. Strain in the Si/SiGe quantum well system partially lifts the valley degeneracy, but the materials factors that set the splitting of the two lowest lying valleys are still…

Mesoscale and Nanoscale Physics · Physics 2016-11-15 Guido Burkard , J. R. Petta

The valley splitting in Si two-dimensional electron systems is studied using Si/SiGe single quantum wells (QWs) with different well widths. The energy gaps for 4 and 5.3 nm QWs, obtained from the temperature dependence of the longitudinal…

Mesoscale and Nanoscale Physics · Physics 2015-05-14 Kohei Sasaki , Ryuichi Masutomi , Kiyohiko Toyama , Kentarou Sawano , Yasuhiro Shiraki , Tohru Okamoto

Valley splitting in strained Si/SiGe quantum wells is a central parameter for silicon spin qubits and is commonly described with envelope-function and effective-mass theories. These models provide a computationally efficient continuum…

Mesoscale and Nanoscale Physics · Physics 2026-02-17 Lasse Ermoneit , Abel Thayil , Thomas Koprucki , Markus Kantner

Motivated by theoretical predictions that spatially complex concentration modulations of Si and Ge can increase the valley splitting in quantum wells, we grow and characterize Si/SiGe heterostructures with a thin, pure Ge layer at the top…

The performance and scalability of silicon spin qubits depend directly on the value of the conduction band valley splitting. In this work, we investigate the influence of electromagnetic fields and the interface width on the valley…

Mesoscale and Nanoscale Physics · Physics 2024-05-07 Jonas R. F. Lima , Guido Burkard

Spin and valley-orbit splittings are calculated in SiGe/Si/SiGe quantum wells (QWs) by using the tight-binding approach. In accordance with the symmetry considerations an existence of spin splitting of electronic states in perfect QWs with…

Mesoscale and Nanoscale Physics · Physics 2008-10-07 M. O. Nestoklon , L. E. Golub , E. L. Ivchenko

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field $B$ and Hall density by…

Silicon/silicon-germanium heterostructures have many important advantages for hosting spin qubits. However, controlling the valley splitting (the energy splitting between the two low-lying conduction-band valleys) remains a critical…

Mesoscale and Nanoscale Physics · Physics 2024-01-12 Merritt P. Losert , M. A. Eriksson , Robert Joynt , Rajib Rahman , Giordano Scappucci , Susan N. Coppersmith , Mark Friesen

We discuss the choice and implementation of inter-valley potentials in the so-called two bands $\mathbf{k}\cdot\mathbf{p}$ model for the opposite $X$, $Y$ or $Z$ valleys of silicon. We focus on the description of valley splittings in…

Mesoscale and Nanoscale Physics · Physics 2026-03-06 Tancredi Salamone , Biel Martinez Diaz , Jing Li , Lukas Cvitkovich , Yann-Michel Niquet

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with…

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk bandstructure of silicon, which has six degenerate electronic minima. The degeneracy can…

Mesoscale and Nanoscale Physics · Physics 2021-05-05 F. Borjans , X. Zhang , X. Mi , G. Cheng , N. Yao , C. A. C. Jackson , L. F. Edge , J. R. Petta

Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting…

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